Summary Stats

Summary Stats

summary(data_short)

##        id              Bank           Year            TA           
##  Min.   :  1.00   AMRB.OQ:   9   Min.   :2010   Min.   :5.789e+08  
##  1st Qu.: 37.75   FCCO.OQ:   9   1st Qu.:2012   1st Qu.:3.144e+09  
##  Median : 74.50   BOCH.OQ:   9   Median :2014   Median :6.760e+09  
##  Mean   : 74.50   SHBI.OQ:   9   Mean   :2014   Mean   :7.744e+10  
##  3rd Qu.:111.25   CVCY.OQ:   9   3rd Qu.:2016   3rd Qu.:1.820e+10  
##  Max.   :148.00   PROV.OQ:   9   Max.   :2018   Max.   :2.620e+12  
##                   (Other):1278                                     
##       RoE                RoA               LtD           LoanstoTA     
##  Min.   :-137.870   Min.   :-6.1400   Min.   :0.2480   Min.   :0.2168  
##  1st Qu.:   6.815   1st Qu.: 0.7850   1st Qu.:0.7626   1st Qu.:0.5997  
##  Median :   8.945   Median : 0.9918   Median :0.8789   Median :0.6797  
##  Mean   :   8.436   Mean   : 0.9498   Mean   :0.8673   Mean   :0.6595  
##  3rd Qu.:  10.880   3rd Qu.: 1.1941   3rd Qu.:0.9599   3rd Qu.:0.7399  
##  Max.   :  43.150   Max.   : 5.7000   Max.   :5.4337   Max.   :0.9372  
##                                                                        
##  NonIntInc_pct        Efficiency     LeverageRatio     T1LeverageRatio 
##  Min.   :-0.09472   Min.   : 29.33   Min.   :0.01677   Min.   :0.0670  
##  1st Qu.: 0.14594   1st Qu.: 57.32   1st Qu.:0.09790   1st Qu.:0.0869  
##  Median : 0.22604   Median : 63.17   Median :0.11154   Median :0.0947  
##  Mean   : 0.22924   Mean   : 63.44   Mean   :0.11319   Mean   :0.0968  
##  3rd Qu.: 0.30118   3rd Qu.: 68.77   3rd Qu.:0.12587   3rd Qu.:0.1034  
##  Max.   : 0.67983   Max.   :172.27   Max.   :0.21597   Max.   :0.1870  
##                                                        NA's   :535     
##      T1_pct      LoanLossProv_pct     NonPerfLoans_pct  LongTermDebt_pct  
##  Min.   : 6.00   Min.   :-0.0197099   Min.   :0.00000   Min.   :0.000000  
##  1st Qu.:11.64   1st Qu.: 0.0009734   1st Qu.:0.00618   1st Qu.:0.007038  
##  Median :12.93   Median : 0.0022666   Median :0.01243   Median :0.017296  
##  Mean   :13.58   Mean   : 0.0045573   Mean   :0.01934   Mean   :0.030290  
##  3rd Qu.:14.55   3rd Qu.: 0.0047699   3rd Qu.:0.02455   3rd Qu.:0.029517  
##  Max.   :42.75   Max.   : 0.0735433   Max.   :0.18231   Max.   :0.799814  
##  NA's   :61                           NA's   :126                         
##    Inflation         GDP_pct          FED_rate      
##  Min.   :0.1186   Min.   :0.8162   Min.   :0.08917  
##  1st Qu.:1.4648   1st Qu.:1.1385   1st Qu.:0.10750  
##  Median :1.6400   Median :1.5644   Median :0.14000  
##  Mean   :1.7674   Mean   :1.5214   Mean   :0.44157  
##  3rd Qu.:2.1301   3rd Qu.:1.7167   3rd Qu.:0.39500  
##  Max.   :3.1568   Max.   :2.2917   Max.   :1.83167  
## 

describe(data_short %>% select(-1, -2, -3))

## data_short %>% select(-1, -2, -3) 
## 
##  16  Variables      1332  Observations
## --------------------------------------------------------------------------------
## TA 
##         n   missing  distinct      Info      Mean       Gmd       .05       .10 
##      1332         0      1317         1 7.744e+10 1.382e+11 1.267e+09 1.582e+09 
##       .25       .50       .75       .90       .95 
## 3.144e+09 6.760e+09 1.820e+10 6.521e+10 2.060e+11 
## 
## lowest : 5.78940e+08 5.81518e+08 5.92753e+08 5.93887e+08 5.96389e+08
## highest: 2.42000e+12 2.49000e+12 2.53000e+12 2.57000e+12 2.62000e+12
## --------------------------------------------------------------------------------
## RoE 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1332        0     1281        1    8.436    4.936    2.160    4.275 
##      .25      .50      .75      .90      .95 
##    6.815    8.945   10.880   13.000   14.788 
## 
## lowest : -137.87000  -58.60000  -34.52250  -34.33186  -34.09000
## highest:   23.93000   24.80000   25.40000   40.60000   43.15000
## --------------------------------------------------------------------------------
## RoA 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1332        0     1050        1   0.9498    0.489   0.2395   0.4925 
##      .25      .50      .75      .90      .95 
##   0.7850   0.9918   1.1941   1.4100   1.6033 
## 
## lowest : -6.14000 -2.85000 -2.57669 -1.80760 -1.77500
## highest:  2.94000  3.09800  3.10500  3.17167  5.70000
## --------------------------------------------------------------------------------
## LtD 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1332        0     1332        1   0.8673    0.193   0.5634   0.6486 
##      .25      .50      .75      .90      .95 
##   0.7626   0.8789   0.9599   1.0313   1.1211 
## 
## lowest : 0.2480464 0.2667948 0.2875208 0.3377034 0.3851405
## highest: 1.5155728 1.5236227 2.1023991 3.1134590 5.4337110
## --------------------------------------------------------------------------------
## LoanstoTA 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1332        0     1332        1   0.6595   0.1305   0.4194   0.4907 
##      .25      .50      .75      .90      .95 
##   0.5997   0.6797   0.7399   0.7867   0.8196 
## 
## lowest : 0.2167902 0.2336244 0.2520854 0.2918288 0.2966595
## highest: 0.9147092 0.9148993 0.9171238 0.9317139 0.9371815
## --------------------------------------------------------------------------------
## NonIntInc_pct 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1332        0     1332        1   0.2292   0.1286  0.05414  0.08317 
##      .25      .50      .75      .90      .95 
##  0.14594  0.22604  0.30118  0.38163  0.42704 
## 
## lowest : -0.09472074 -0.03836141 -0.02688185 -0.02324207 -0.01025759
## highest:  0.63002153  0.64343266  0.64481168  0.66360437  0.67982548
## --------------------------------------------------------------------------------
## Efficiency 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1332        0     1332        1    63.44    12.51    44.11    49.19 
##      .25      .50      .75      .90      .95 
##    57.32    63.17    68.77    76.09    83.39 
## 
## lowest :  29.32553  31.66164  33.49141  33.64349  33.75433
## highest: 109.43046 123.75694 129.26516 152.02659 172.26959
## --------------------------------------------------------------------------------
## LeverageRatio 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1332        0     1332        1   0.1132  0.02422  0.08244  0.08851 
##      .25      .50      .75      .90      .95 
##  0.09790  0.11154  0.12587  0.13903  0.15344 
## 
## lowest : 0.01677276 0.03546389 0.03811750 0.03952972 0.04298529
## highest: 0.19914474 0.20480579 0.20657599 0.20846264 0.21597261
## --------------------------------------------------------------------------------
## T1LeverageRatio 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##      797      535      797        1  0.09683    0.016  0.07632  0.08052 
##      .25      .50      .75      .90      .95 
##  0.08693  0.09469  0.10344  0.11496  0.12264 
## 
## lowest : 0.06696443 0.06773576 0.06779661 0.06859491 0.06859504
## highest: 0.16263428 0.16848997 0.17113544 0.17938062 0.18704062
## --------------------------------------------------------------------------------
## T1_pct 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1271       61      650        1    13.58    3.129    10.21    10.65 
##      .25      .50      .75      .90      .95 
##    11.64    12.93    14.55    17.33    19.05 
## 
## lowest :  6.00  6.09  6.21  6.81  6.90, highest: 31.75 33.03 36.57 38.47 42.75
## --------------------------------------------------------------------------------
## LoanLossProv_pct 
##          n    missing   distinct       Info       Mean        Gmd        .05 
##       1332          0       1308          1   0.004557   0.006311 -0.0010828 
##        .10        .25        .50        .75        .90        .95 
##  0.0000000  0.0009734  0.0022666  0.0047699  0.0121358  0.0187905 
## 
## lowest : -0.019709879 -0.008568730 -0.007767283 -0.007744641 -0.006836029
## highest:  0.060671818  0.061076296  0.067616232  0.068633400  0.073543267
## --------------------------------------------------------------------------------
## NonPerfLoans_pct 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1206      126     1206        1  0.01934  0.01935 0.001918 0.003252 
##      .25      .50      .75      .90      .95 
## 0.006184 0.012429 0.024548 0.042931 0.061888 
## 
## lowest : 0.000000e+00 4.584461e-05 5.772795e-05 8.362473e-05 1.594983e-04
## highest: 1.413719e-01 1.440444e-01 1.443116e-01 1.633339e-01 1.823105e-01
## --------------------------------------------------------------------------------
## LongTermDebt_pct 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1332        0     1147    0.997  0.03029  0.03681 0.000000 0.000000 
##      .25      .50      .75      .90      .95 
## 0.007038 0.017296 0.029517 0.082259 0.115229 
## 
## lowest : 0.000000e+00 3.253073e-05 5.163573e-05 7.948689e-05 2.331196e-04
## highest: 3.968581e-01 4.170735e-01 5.756029e-01 7.231403e-01 7.998144e-01
## --------------------------------------------------------------------------------
## Inflation 
##        n  missing distinct     Info     Mean      Gmd 
##     1332        0        9    0.988    1.767   0.8635 
## 
## lowest : 0.1186271 1.2615832 1.4648327 1.6222230 1.6400434
## highest: 1.6400434 2.0693373 2.1301100 2.4425833 3.1568416
##                                                                       
## Value      0.1186271 1.2615832 1.4648327 1.6222230 1.6400434 2.0693373
## Frequency        148       148       148       148       148       148
## Proportion     0.111     0.111     0.111     0.111     0.111     0.111
##                                         
## Value      2.1301100 2.4425833 3.1568416
## Frequency        148       148       148
## Proportion     0.111     0.111     0.111
## --------------------------------------------------------------------------------
## GDP_pct 
##        n  missing distinct     Info     Mean      Gmd 
##     1332        0        9    0.988    1.521     0.55 
## 
## lowest : 0.8162317 0.8351279 1.1384973 1.5021706 1.5644444
## highest: 1.5644444 1.7026342 1.7167482 2.1251228 2.2917295
##                                                                       
## Value      0.8162317 0.8351279 1.1384973 1.5021706 1.5644444 1.7026342
## Frequency        148       148       148       148       148       148
## Proportion     0.111     0.111     0.111     0.111     0.111     0.111
##                                         
## Value      1.7167482 2.1251228 2.2917295
## Frequency        148       148       148
## Proportion     0.111     0.111     0.111
## --------------------------------------------------------------------------------
## FED_rate 
##        n  missing distinct     Info     Mean      Gmd 
##     1332        0        9    0.988   0.4416   0.5084 
## 
## lowest : 0.08916667 0.10166667 0.10750000 0.13250000 0.14000000
## highest: 0.14000000 0.17500000 0.39500000 1.00166667 1.83166667
##                                                                             
## Value      0.08916667 0.10166667 0.10750000 0.13250000 0.14000000 0.17500000
## Frequency         148        148        148        148        148        148
## Proportion      0.111      0.111      0.111      0.111      0.111      0.111
##                                            
## Value      0.39500000 1.00166667 1.83166667
## Frequency         148        148        148
## Proportion      0.111      0.111      0.111
## --------------------------------------------------------------------------------

stargazer(data_short %>% mutate(TA = log(TA)))

## 
## % Table created by stargazer v.5.2.2 by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu
## % Date and time: Sun, Apr 12, 2020 - 11:27:30
## \begin{table}[!htbp] \centering 
##   \caption{} 
##   \label{} 
## \begin{tabular}{@{\extracolsep{5pt}}lccccccc} 
## \\[-1.8ex]\hline 
## \hline \\[-1.8ex] 
## Statistic & \multicolumn{1}{c}{N} & \multicolumn{1}{c}{Mean} & \multicolumn{1}{c}{St. Dev.} & \multicolumn{1}{c}{Min} & \multicolumn{1}{c}{Pctl(25)} & \multicolumn{1}{c}{Pctl(75)} & \multicolumn{1}{c}{Max} \\ 
## \hline \\[-1.8ex] 
## id & 1,332 & 74.500 & 42.739 & 1 & 37.8 & 111.2 & 148 \\ 
## Year & 1,332 & 2,014.000 & 2.583 & 2,010 & 2,012 & 2,016 & 2,018 \\ 
## TA & 1,332 & 22.910 & 1.583 & 20.177 & 21.869 & 23.625 & 28.594 \\ 
## RoE & 1,332 & 8.436 & 6.685 & $-$137.870 & 6.815 & 10.880 & 43.150 \\ 
## RoA & 1,332 & 0.950 & 0.541 & $-$6.140 & 0.785 & 1.194 & 5.700 \\ 
## LtD & 1,332 & 0.867 & 0.220 & 0.248 & 0.763 & 0.960 & 5.434 \\ 
## LoanstoTA & 1,332 & 0.660 & 0.119 & 0.217 & 0.600 & 0.740 & 0.937 \\ 
## NonIntInc\_pct & 1,332 & 0.229 & 0.114 & $-$0.095 & 0.146 & 0.301 & 0.680 \\ 
## Efficiency & 1,332 & 63.439 & 11.995 & 29.326 & 57.323 & 68.771 & 172.270 \\ 
## LeverageRatio & 1,332 & 0.113 & 0.022 & 0.017 & 0.098 & 0.126 & 0.216 \\ 
## T1LeverageRatio & 797 & 0.097 & 0.015 & 0.067 & 0.087 & 0.103 & 0.187 \\ 
## T1\_pct & 1,271 & 13.576 & 3.222 & 6.000 & 11.645 & 14.550 & 42.750 \\ 
## LoanLossProv\_pct & 1,332 & 0.005 & 0.008 & $-$0.020 & 0.001 & 0.005 & 0.074 \\ 
## NonPerfLoans\_pct & 1,206 & 0.019 & 0.021 & 0.000 & 0.006 & 0.025 & 0.182 \\ 
## LongTermDebt\_pct & 1,332 & 0.030 & 0.051 & 0.000 & 0.007 & 0.030 & 0.800 \\ 
## Inflation & 1,332 & 1.767 & 0.797 & 0.119 & 1.465 & 2.130 & 3.157 \\ 
## GDP\_pct & 1,332 & 1.521 & 0.488 & 0.816 & 1.138 & 1.717 & 2.292 \\ 
## FED\_rate & 1,332 & 0.442 & 0.564 & 0.089 & 0.108 & 0.395 & 1.832 \\ 
## \hline \\[-1.8ex] 
## \end{tabular} 
## \end{table}

Winsorised summary statistics

data_stata_win_summary <- data_stata_win_reg %>%
  gather(key = "Variable", value = "Value", TA:LeverageRatio, T1_pct:GDP_pct) %>%
  filter(is.na(Value) != TRUE) %>%
  group_by(Variable) %>%
  summarise(N = n(),
            Mean = round(mean(Value, na.rm = TRUE),2),
            'St. Dev.' = round(sd(Value, na.rm = TRUE),2),
            Min = round(min(Value, na.rm = TRUE),2),
            'Pctl(25)' = round(quantile(Value, 0.25, na.rm = TRUE),2),
            Median = round(quantile(Value, 0.50, na.rm = TRUE),2),
            'Pctl(75)' = round(quantile(Value, 0.75, na.rm = TRUE),2),
            Max = round(max(Value, na.rm = TRUE),2)) 

rownames(data_stata_win_summary) <- data_stata_win_summary$Variable

## Warning: Setting row names on a tibble is deprecated.

data_stata_win_summary <- data_stata_win_summary %>%
  select(-Variable)

stargazer(data_stata_win_summary, summary = FALSE)

## 
## % Table created by stargazer v.5.2.2 by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu
## % Date and time: Sun, Apr 12, 2020 - 11:27:30
## \begin{table}[!htbp] \centering 
##   \caption{} 
##   \label{} 
## \begin{tabular}{@{\extracolsep{5pt}} ccccccccc} 
## \\[-1.8ex]\hline 
## \hline \\[-1.8ex] 
##  & N & Mean & St. Dev. & Min & Pctl(25) & Median & Pctl(75) & Max \\ 
## \hline \\[-1.8ex] 
## Efficiency & 1332 & 63.31 & 11.25 & 34.44 & 57.32 & 63.17 & 68.77 & 102.36 \\ 
## GDP\_pct & 1332 & 1.52 & 0.49 & 0.82 & 1.14 & 1.56 & 1.72 & 2.29 \\ 
## Inflation & 1332 & 1.77 & 0.8 & 0.12 & 1.46 & 1.64 & 2.13 & 3.16 \\ 
## LeverageRatio & 1332 & 11.32 & 2.16 & 6.26 & 9.79 & 11.15 & 12.59 & 19.06 \\ 
## LoanLossProv\_pct & 1332 & 0.45 & 0.74 & -0.55 & 0.1 & 0.23 & 0.48 & 5.24 \\ 
## LoanstoTA & 1332 & 65.97 & 11.78 & 31.1 & 59.97 & 67.97 & 73.99 & 91.33 \\ 
## LongTermDebt\_pct & 1332 & 2.9 & 3.87 & 0 & 0.7 & 1.73 & 2.95 & 23.68 \\ 
## LtD & 1332 & 86.3 & 16.72 & 41.71 & 76.26 & 87.89 & 95.99 & 147.67 \\ 
## NonIntInc\_pct & 1332 & 22.91 & 11.3 & 0.9 & 14.59 & 22.6 & 30.12 & 57.81 \\ 
## NonPerfLoans\_pct & 1206 & 1.92 & 2.01 & 0.04 & 0.62 & 1.24 & 2.45 & 12.38 \\ 
## RoA & 1332 & 0.95 & 0.47 & -1.61 & 0.78 & 0.99 & 1.19 & 2.21 \\ 
## RoE & 1332 & 8.55 & 4.74 & -20.99 & 6.81 & 8.95 & 10.88 & 22.64 \\ 
## T1\_pct & 1271 & 13.56 & 3.02 & 8.6 & 11.64 & 12.93 & 14.55 & 29.68 \\ 
## TA & 1332 & 22.91 & 1.58 & 20.18 & 21.87 & 22.63 & 23.62 & 28.59 \\ 
## \hline \\[-1.8ex] 
## \end{tabular} 
## \end{table}

With est_RW

data_stata_win_summary <- data_stata_win_reg %>%
  gather(key = "Variable", value = "Value", TA:LeverageRatio, T1_pct:GDP_pct, est_RW) %>%
  filter(is.na(Value) != TRUE) %>%
  group_by(Variable) %>%
  summarise(N = n(),
            Mean = round(mean(Value, na.rm = TRUE),2),
            'St. Dev.' = round(sd(Value, na.rm = TRUE),2),
            Min = round(min(Value, na.rm = TRUE),2),
            'Pctl(25)' = round(quantile(Value, 0.25, na.rm = TRUE),2),
            Median = round(quantile(Value, 0.50, na.rm = TRUE),2),
            'Pctl(75)' = round(quantile(Value, 0.75, na.rm = TRUE),2),
            Max = round(max(Value, na.rm = TRUE),2)) 

rownames(data_stata_win_summary) <- data_stata_win_summary$Variable

## Warning: Setting row names on a tibble is deprecated.

data_stata_win_summary <- data_stata_win_summary %>%
  select(-Variable)

stargazer(data_stata_win_summary, summary = FALSE)

## 
## % Table created by stargazer v.5.2.2 by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu
## % Date and time: Sun, Apr 12, 2020 - 11:27:30
## \begin{table}[!htbp] \centering 
##   \caption{} 
##   \label{} 
## \begin{tabular}{@{\extracolsep{5pt}} ccccccccc} 
## \\[-1.8ex]\hline 
## \hline \\[-1.8ex] 
##  & N & Mean & St. Dev. & Min & Pctl(25) & Median & Pctl(75) & Max \\ 
## \hline \\[-1.8ex] 
## Efficiency & 1332 & 63.31 & 11.25 & 34.44 & 57.32 & 63.17 & 68.77 & 102.36 \\ 
## est\_RW & 1271 & 72.28 & 12.94 & 30.68 & 63.84 & 72.79 & 80.51 & 123.51 \\ 
## GDP\_pct & 1332 & 1.52 & 0.49 & 0.82 & 1.14 & 1.56 & 1.72 & 2.29 \\ 
## Inflation & 1332 & 1.77 & 0.8 & 0.12 & 1.46 & 1.64 & 2.13 & 3.16 \\ 
## LeverageRatio & 1332 & 11.32 & 2.16 & 6.26 & 9.79 & 11.15 & 12.59 & 19.06 \\ 
## LoanLossProv\_pct & 1332 & 0.45 & 0.74 & -0.55 & 0.1 & 0.23 & 0.48 & 5.24 \\ 
## LoanstoTA & 1332 & 65.97 & 11.78 & 31.1 & 59.97 & 67.97 & 73.99 & 91.33 \\ 
## LongTermDebt\_pct & 1332 & 2.9 & 3.87 & 0 & 0.7 & 1.73 & 2.95 & 23.68 \\ 
## LtD & 1332 & 86.3 & 16.72 & 41.71 & 76.26 & 87.89 & 95.99 & 147.67 \\ 
## NonIntInc\_pct & 1332 & 22.91 & 11.3 & 0.9 & 14.59 & 22.6 & 30.12 & 57.81 \\ 
## NonPerfLoans\_pct & 1206 & 1.92 & 2.01 & 0.04 & 0.62 & 1.24 & 2.45 & 12.38 \\ 
## RoA & 1332 & 0.95 & 0.47 & -1.61 & 0.78 & 0.99 & 1.19 & 2.21 \\ 
## RoE & 1332 & 8.55 & 4.74 & -20.99 & 6.81 & 8.95 & 10.88 & 22.64 \\ 
## T1\_pct & 1271 & 13.56 & 3.02 & 8.6 & 11.64 & 12.93 & 14.55 & 29.68 \\ 
## TA & 1332 & 22.91 & 1.58 & 20.18 & 21.87 & 22.63 & 23.62 & 28.59 \\ 
## \hline \\[-1.8ex] 
## \end{tabular} 
## \end{table}

Correlation Matrix

Variables of interest

Just 2018

corrplot(cor_select, order = "hclust", 
         tl.col = "black", tl.srt = 45)

Variables used in regression

Just 2018

corrplot(cor_stata_win, order = "hclust", 
         tl.col = "black", tl.srt = 45)

All years, winsorised sample

corrplot(cor_stata_win, order = "hclust", 
         tl.col = "black", tl.srt = 45)

cor_stata_win_diag <- cor_stata_win
diag(cor_stata_win_diag) = NA

corrplot(cor_stata_win_diag, order = "hclust", 
         tl.col = "black", tl.srt = 45,
         method = "color", na.label = "-",
         p.mat = rcor_stata_win$P,
         insig = "label_sig", sig.level = c(.001, .01, .05), pch.cex = .8, pch.col = "black")

Average of each year’s correlation

corrplot(cor_stata_win_year, order = "hclust", 
         tl.col = "black", tl.srt = 45)

cor_stata_win_year_diag <- cor_stata_win_year
diag(cor_stata_win_year_diag) = NA

corrplot(cor_stata_win_year_diag, order = "hclust",
         tl.col = "black", tl.srt = 45,
         method = "color", na.label = "-")

Correlation over time

ROE

cor_stata_win_year_DF %>%
  ggplot(aes(x = Year, y = RoE, colour = Variable, group = Variable)) + 
  geom_line(size = 1) +
  scale_x_continuous(expand = c(0.15, 0.15), breaks = seq(2010, 2018, 2)
                     ) +
  geom_dl(aes(label = Variable), method = list(dl.combine("first.points", "last.points"), cex = 0.6)) +
  labs(y = "Correlation with RoE")

ROA

cor_stata_win_year_DF %>%
  ggplot(aes(x = Year, y = RoA, colour = Variable, group = Variable)) + 
  geom_line(size = 1) +
  scale_x_continuous(expand = c(0.15, 0.15), breaks = seq(2010, 2018, 2)
                     ) +
  geom_dl(aes(label = Variable), method = list(dl.combine("first.points", "last.points"), cex = 0.6)) +
  labs(y = "Correlation with RoE")

TA

cor_stata_win_year_DF %>%
  ggplot(aes(x = Year, y = TA, colour = Variable, group = Variable)) + 
  geom_line(size = 1) +
  scale_x_continuous(expand = c(0.15, 0.15), breaks = seq(2010, 2018, 2)
                     ) +
  geom_dl(aes(label = Variable), method = list(dl.combine("first.points", "last.points"), cex = 0.6)) +
  labs(y = "Correlation with RoE")

T1_pct

cor_stata_win_year_DF %>%
  ggplot(aes(x = Year, y = T1_pct, colour = Variable, group = Variable)) + 
  geom_line(size = 1) +
  scale_x_continuous(expand = c(0.15, 0.15), breaks = seq(2010, 2018, 2)
                     ) +
  geom_dl(aes(label = Variable), method = list(dl.combine("first.points", "last.points"), cex = 0.6)) +
  labs(y = "Correlation with RoE")

Loan Loss Provision

cor_stata_win_year_DF %>%
  ggplot(aes(x = Year, y = LoanLossProv_pct, colour = Variable, group = Variable)) + 
  geom_line(size = 1) +
  scale_x_continuous(expand = c(0.15, 0.15), breaks = seq(2010, 2018, 2)
                     ) +
  geom_dl(aes(label = Variable), method = list(dl.combine("first.points", "last.points"), cex = 0.6)) +
  labs(y = "Correlation with RoE")

Z-score over time

data_stata_z %>%
  gather(key = "variable", value = "value", TA:LeverageRatio, T1_pct:GDP_pct, est_RW) %>%
  group_by(Year, variable) %>%
  summarise(value = mean(value, na.rm = TRUE)) %>%
  filter(variable != "Inflation" & variable != "GDP_pct") %>%
  ggplot(aes(x = Year, y = value, colour = variable, group = variable)) + 
  geom_line(size = 0.9) +
  scale_x_continuous(expand = c(0.15, 0.15), breaks = seq(2010, 2018, 2)) +
  geom_dl(aes(label = variable), method = list(dl.combine("first.points", "last.points"), cex = 0.6)) +
  labs(y = "Z-Score")

Variable over time (free scale facet)

data_stata_win %>%
  mutate(TA = log(TA),
         LoanstoTA = LoanstoTA*100,
         NonIntInc_pct = NonIntInc_pct*100,
         T1LeverageRatio = T1LeverageRatio*100,
         LoanLossProv_pct = LoanLossProv_pct*100,
         NonPerfLoans_pct = NonPerfLoans_pct*100,
         LongTermDebt_pct = LongTermDebt_pct*100,
         LtD = LtD*100,
         LeverageRatio = LeverageRatio*100) %>%
  gather(key = "variable", value = "value", TA:LeverageRatio, T1_pct:GDP_pct) %>%
  group_by(Year, variable) %>%
  summarise(mean = mean(value, na.rm = TRUE)) %>%
  filter(variable != "Inflation" & variable != "GDP_pct") %>%
  mutate(variable = as.factor(variable),
         variable = factor(variable, levels(variable)[c(10, 9, 12, 1, 7, 2, 11, 3, 8, 6, 4, 5)],
                           labels = c("RoE", "RoA", "ln(TA)", "Efficiency", "Non-interest income", "Leverage Ratio", "T1 (% RWAs)", "Loan Loss Provisions", "Non-performing Loans", "Loans to Deposits", "Loans to Total Assets", "Long-term Debt"))) %>%
  ggplot(aes(x = Year, y = mean, colour = variable, group = variable)) + 
  geom_line(size = 0.9) +
  scale_x_continuous(breaks = seq(2010, 2018, 4)) +
  facet_wrap(~ variable, scales = "free") +
  theme(legend.position = "none",
        axis.title.x = element_blank()) +
  labs(title = "Change in mean value for each variable over time", y = "mean 
       ")

data_stata_win %>%
  mutate(TA = log(TA),
         LoanstoTA = LoanstoTA*100,
         NonIntInc_pct = NonIntInc_pct*100,
         T1LeverageRatio = T1LeverageRatio*100,
         LoanLossProv_pct = LoanLossProv_pct*100,
         NonPerfLoans_pct = NonPerfLoans_pct*100,
         LongTermDebt_pct = LongTermDebt_pct*100,
         LtD = LtD*100,
         LeverageRatio = LeverageRatio*100) %>%
  gather(key = "variable", value = "value", TA:LeverageRatio, T1_pct:GDP_pct) %>%
  group_by(Year, variable) %>%
  summarise(median = median(value, na.rm = TRUE),
            first = quantile(value, 0.25, na.rm = TRUE),
            third = quantile(value, 0.75, na.rm = TRUE)) %>%
  filter(variable != "Inflation" & variable != "GDP_pct") %>%
  mutate(variable = as.factor(variable),
         variable = factor(variable, levels(variable)[c(10, 9, 12, 1, 7, 2, 11, 3, 8, 6, 4, 5)],
                           labels = c("RoE", "RoA", "ln(TA)", "Efficiency", "Non-interest income", "Leverage Ratio", "T1 (% RWAs)", "Loan Loss Provisions", "Non-performing Loans", "Loans to Deposits", "Loans to Total Assets", "Long-term Debt"))) %>%
  ggplot(aes(x = Year, y = median, colour = variable, group = variable)) + 
  geom_line(size = 0.9) +
  geom_line(aes(y = first), alpha = 0.3, size = 0.9) +
  geom_line(aes(y = third), alpha = 0.3, size = 0.9) +
  scale_x_continuous(breaks = seq(2010, 2018, 4)) +
  facet_wrap(~ variable, scales = "free") +
  theme(legend.position = "none",
        axis.title.x = element_blank()) +
  labs(title = "Change in median and IQR for each variable over time", y = "Median and IQR 
       ")

data_stata_win %>%
  mutate(TA = log(TA),
         LoanstoTA = LoanstoTA*100,
         NonIntInc_pct = NonIntInc_pct*100,
         T1LeverageRatio = T1LeverageRatio*100,
         LoanLossProv_pct = LoanLossProv_pct*100,
         NonPerfLoans_pct = NonPerfLoans_pct*100,
         LongTermDebt_pct = LongTermDebt_pct*100,
         LtD = LtD*100,
         LeverageRatio = LeverageRatio*100) %>%
  gather(key = "variable", value = "value", TA:LeverageRatio, T1_pct:GDP_pct) %>%
  filter(variable != "Inflation" & variable != "GDP_pct") %>%
  mutate(variable = as.factor(variable),
         variable = factor(variable, levels(variable)[c(10, 9, 12, 1, 7, 2, 11, 3, 8, 6, 4, 5)],
                           labels = c("RoE", "RoA", "ln(TA)", "Efficiency", "Non-interest income", "Leverage Ratio", "T1 (% RWAs)", "Loan Loss Provisions", "Non-performing Loans", "Loans to Deposits", "Loans to Total Assets", "Long-term Debt"))) %>%
  ggplot(aes(x = Year, y = value, fill = variable, group = Year)) + 
  geom_boxplot(outlier.colour = "grey") +
  scale_x_continuous(breaks = seq(2010, 2018, 4)) +
  facet_wrap(~ variable, scales = "free") +
  theme(legend.position = "none",
        axis.title.x = element_blank(),
        axis.title.y = element_blank())

## Warning: Removed 187 rows containing non-finite values (stat_boxplot).

Box Plots

Dependent Variables

RoE

data %>%
  ggplot(aes(x = Year, y = RoE, group = Year)) +
  geom_boxplot() +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

RoA

data %>%
  ggplot(aes(x = Year, y = RoA, group = Year)) +
  geom_boxplot() +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

Independent Variables

Size (Total Assets - Log)

data %>%
  ggplot(aes(x = Year, y = TA, group = Year)) +
  geom_boxplot() +
  scale_y_log10() +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

Credit Quality (Loan Loss Provision as % of Loans)

data %>%
  ggplot(aes(x = Year, y = LoanLossProv_pct, group = Year)) +
  geom_boxplot() +
  scale_y_continuous(labels = percent_format()) +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

Credit Quality (Non-performing loans as % of Loans) # some NAs

data %>%
  ggplot(aes(x = Year, y = NonPerfLoans_pct, group = Year)) +
  geom_boxplot() +
  scale_y_continuous(labels = percent_format()) +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

## Warning: Removed 126 rows containing non-finite values (stat_boxplot).

Managment Efficiency (Cost of Revenue)

data %>%
  ggplot(aes(x = Year, y = Efficiency, group = Year)) +
  geom_boxplot() +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

Capitalisation (Tier 1 capital as % of Risk-weighted Assets)

data %>%
  ggplot(aes(x = Year, y = T1_pct, group = Year)) +
  geom_boxplot() +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

Capitalisation (Capital as % of Total Assets)

data %>%
  ggplot(aes(x = Year, y = LeverageRatio, group = Year)) +
  geom_boxplot() +
  scale_y_continuous(labels = percent_format()) +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

Estimated Risk-Weight

data_stata %>%
  ggplot(aes(x = Year, y = est_RW, group = Year)) +
  geom_boxplot() +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

## Warning: Removed 61 rows containing non-finite values (stat_boxplot).

Diversification (% of Non-Interest Income)

data %>%
  ggplot(aes(x = Year, y = NonIntInc_pct, group = Year)) +
  geom_boxplot() +
  scale_y_continuous(labels = percent_format()) +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

Liquidity proxy (Loans to Deposits)

data %>%
  ggplot(aes(x = Year, y = LtD, group = Year)) +
  geom_boxplot() +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

Financing (Long-term Debt as % of Total Assets)

data %>%
  ggplot(aes(x = Year, y = LongTermDebt_pct, group = Year)) +
  geom_boxplot() +
  scale_y_continuous(labels = percent_format()) +
  scale_x_continuous(breaks = seq(2010, 2018, 1))

Histograms

Dependent Variables

RoE

data %>%
  ggplot(aes(x = RoE)) +
  geom_histogram(bins = 75) +
  facet_wrap(~ Year) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.RoE = mean(RoE)), aes(xintercept = mean.RoE), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.RoE = quantile(RoE, 0.25)), aes(xintercept = st.RoE), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.RoE = quantile(RoE, 0.75)), aes(xintercept = rd.RoE), linetype = "dashed", col = "orange")

RoA

data %>%
  ggplot(aes(x = RoA)) +
  geom_histogram(bins = 75) +
  facet_wrap(~ Year) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.RoA = mean(RoA)), aes(xintercept = mean.RoA), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.RoA = quantile(RoA, 0.25)), aes(xintercept = st.RoA), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.RoA = quantile(RoA, 0.75)), aes(xintercept = rd.RoA), linetype = "dashed", col = "orange")

Independent Variables

Size (Total Assets - Log)

data %>%
  ggplot(aes(x = TA)) +
  geom_histogram(bins = 75) +
  scale_x_log10() +
  facet_wrap(~ Year) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.TA = mean(TA, na.rm = TRUE)), aes(xintercept = mean.TA), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.TA = quantile(TA, 0.25, na.rm = TRUE)), aes(xintercept = st.TA), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.TA = quantile(TA, 0.75, na.rm = TRUE)), aes(xintercept = rd.TA), linetype = "dashed", col = "orange")

Credit Quality (Loan Loss Provision as % of Loans)

data %>%
  ggplot(aes(x = LoanLossProv_pct)) +
  geom_histogram(bins = 75) +
  facet_wrap(~ Year) +
  scale_x_continuous(labels = percent_format()) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.LoanLossProv_pct = mean(LoanLossProv_pct, na.rm = TRUE)), aes(xintercept = mean.LoanLossProv_pct), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.LoanLossProv_pct = quantile(LoanLossProv_pct, 0.25, na.rm = TRUE)), aes(xintercept = st.LoanLossProv_pct), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.LoanLossProv_pct = quantile(LoanLossProv_pct, 0.75, na.rm = TRUE)), aes(xintercept = rd.LoanLossProv_pct), linetype = "dashed", col = "orange")

Credit Quality (Non-performing Loans as % of Loans)

data %>%
  ggplot(aes(x = NonPerfLoans_pct)) +
  geom_histogram(bins = 75) +
  facet_wrap(~ Year) +
  scale_x_continuous(labels = percent_format()) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.LoanLossProv_pct = mean(LoanLossProv_pct, na.rm = TRUE)), aes(xintercept = mean.LoanLossProv_pct), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.LoanLossProv_pct = quantile(LoanLossProv_pct, 0.25, na.rm = TRUE)), aes(xintercept = st.LoanLossProv_pct), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.LoanLossProv_pct = quantile(LoanLossProv_pct, 0.75, na.rm = TRUE)), aes(xintercept = rd.LoanLossProv_pct), linetype = "dashed", col = "orange")

## Warning: Removed 126 rows containing non-finite values (stat_bin).

Managment Efficiency (Cost of Revenue)

data %>%
  ggplot(aes(x = Efficiency)) +
  geom_histogram(bins = 75) +
  xlim(0,180) +
  facet_wrap(~ Year) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.Efficiency = mean(Efficiency)), aes(xintercept = mean.Efficiency), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.Efficiency = quantile(Efficiency, 0.25)), aes(xintercept = st.Efficiency), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.Efficiency = quantile(Efficiency, 0.75)), aes(xintercept = rd.Efficiency), linetype = "dashed", col = "orange")

Capitalisation (Tier 1 capital as % of Risk-weighted Assets)

data %>%
  ggplot(aes(x = T1_pct)) +
  geom_histogram(bins = 75) +
  facet_wrap(~ Year) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.T1_pct = mean(T1_pct, na.rm = TRUE)), aes(xintercept = mean.T1_pct), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.T1_pct = quantile(T1_pct, 0.25, na.rm = TRUE)), aes(xintercept = st.T1_pct), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.T1_pct = quantile(T1_pct, 0.75, na.rm = TRUE)), aes(xintercept = rd.T1_pct), linetype = "dashed", col = "orange")

Capitalisation (Capital as % of Total Assets)

data %>%
  ggplot(aes(x = LeverageRatio)) +
  geom_histogram(bins = 75) +
  facet_wrap(~ Year) +
  scale_x_continuous(labels = percent_format()) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.LeverageRatio = mean(LeverageRatio, na.rm = TRUE)), aes(xintercept = mean.LeverageRatio), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.LeverageRatio = quantile(LeverageRatio, 0.25, na.rm = TRUE)), aes(xintercept = st.LeverageRatio), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.LeverageRatio = quantile(LeverageRatio, 0.75, na.rm = TRUE)), aes(xintercept = rd.LeverageRatio), linetype = "dashed", col = "orange")

Diversification (% of Non-Interest Income)

data %>%
  ggplot(aes(x = NonIntInc_pct)) +
  geom_histogram(bins = 75) +
  facet_wrap(~ Year) +
  scale_x_continuous(labels = percent_format()) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.NonIntInc_pct = mean(NonIntInc_pct, na.rm = TRUE)), aes(xintercept = mean.NonIntInc_pct), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.NonIntInc_pct = quantile(NonIntInc_pct, 0.25, na.rm = TRUE)), aes(xintercept = st.NonIntInc_pct), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.NonIntInc_pct = quantile(NonIntInc_pct, 0.75, na.rm = TRUE)), aes(xintercept = rd.NonIntInc_pct), linetype = "dashed", col = "orange")

Liquidity proxy (Loans to Deposits)

data %>%
  ggplot(aes(x = LtD)) +
  geom_histogram(bins = 75) +
  facet_wrap(~ Year) +
  scale_x_continuous(labels = percent_format()) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.LtD = mean(LtD, na.rm = TRUE)), aes(xintercept = mean.LtD), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.LtD = quantile(LtD, 0.25, na.rm = TRUE)), aes(xintercept = st.LtD), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.LtD = quantile(LtD, 0.75, na.rm = TRUE)), aes(xintercept = rd.LtD), linetype = "dashed", col = "orange")

Financing (Long-term Debt as % of Total Assets)

data %>%
  ggplot(aes(x = LongTermDebt_pct)) +
  geom_histogram(bins = 75) +
  facet_wrap(~ Year) +
  scale_x_continuous(labels = percent_format()) +
  geom_vline(data = data %>% group_by(Year) %>% summarise(mean.LongTermDebt_pct = mean(LongTermDebt_pct, na.rm = TRUE)), aes(xintercept = mean.LongTermDebt_pct), linetype = "dashed", col = "red") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(st.LongTermDebt_pct = quantile(LongTermDebt_pct, 0.25, na.rm = TRUE)), aes(xintercept = st.LongTermDebt_pct), linetype = "dashed", col = "orange") +
  geom_vline(data = data %>% group_by(Year) %>% summarise(rd.LongTermDebt_pct = quantile(LongTermDebt_pct, 0.75, na.rm = TRUE)), aes(xintercept = rd.LongTermDebt_pct), linetype = "dashed", col = "orange")

Outliers

residual %>%
  ggplot(aes(x = r)) +
  geom_histogram(bins = 75) +
  scale_x_continuous(breaks = seq(-100, 100, 10))

## Warning: Removed 61 rows containing non-finite values (stat_bin).

group by RoE category

Top half RoE

data_stata_z_gather %>%
  filter(variable != "Inflation" & variable != "GDP_pct" & variable != "T1LeverageRatio") %>%
  mutate(variable = as.factor(variable),
         variable = factor(variable, levels(variable)[c(11, 10, 13, 3, 12, 4, 9, 7, 5, 6, 8, 1, 2)])) %>%
  ggplot(aes(y = value, x = variable, fill = factor(RoE_top_50))) +
  geom_boxplot(outlier.colour = NA) +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5),
        axis.title.x = element_blank()) +
  labs(y = "z-score", fill = "RoE in top 50%")

## Warning: Removed 248 rows containing non-finite values (stat_boxplot).

By RoE quartiles

data_stata_z_gather %>%
  filter(variable != "Inflation" & variable != "GDP_pct" & variable != "T1LeverageRatio") %>%
  mutate(variable = as.factor(variable),
         variable = factor(variable, levels(variable)[c(11, 10, 13, 3, 12, 4, 9, 7, 5, 6, 8, 1, 2)])) %>%
  ggplot(aes(y = value, x = variable, fill = factor(RoE_quartiles))) +
  geom_boxplot(outlier.colour = NA) +
  theme(axis.text.x = element_text(angle = 45, vjust = 0.9, hjust = 0.9),
        axis.title.x = element_blank()) +
  scale_fill_discrete(name = "RoE by quartiles", labels = c("1st quartile", "2nd quartile", "3rd quartile", "4th quartile")) + 
  scale_x_discrete(labels=c("TA" = "ln(TA)", "LeverageRatio" = "Leverage Ratio", "T1_pct" = "T1 (% RWAs)",
                              "LoanLossProv_pct" = "Loan Loss Provisions", "NonPerfLoans_pct" = "Non-performing Loans", "LtD" = "Loans to Deposits", "LoanstoTA" = "Loans to Total Assets", "LongTermDebt_pct" = "Long-term Debt", "NonIntInc_pct" = "Non-interest income", "est_RW" = "average risk-weight")) +
  labs(y = "z-score", fill = "RoE by quartiles")

## Warning: Removed 248 rows containing non-finite values (stat_boxplot).

Z-score

data_stata_z_gather %>%
  filter(variable != "Inflation" & variable != "GDP_pct" & variable != "T1LeverageRatio" & variable != "est_RW") %>%
  mutate(variable = as.factor(variable),
         variable = factor(variable, levels(variable)[c(10, 9, 12, 1, 7, 2, 11, 3, 8, 6, 4, 5)],
                           labels = c("RoE", "RoA", "ln(TA)", "Efficiency", "Non-interest income", "Leverage Ratio", "T1 (% RWAs)", "Loan Loss Provisions", "Non-performing Loans", "Loans to Deposits", "Loans to Total Assets", "Long-term Debt"))) %>%
  ggplot(aes(y = value, x = variable, fill = factor(RoE_quartiles))) +
  geom_boxplot(outlier.colour = "grey") +
  scale_fill_discrete(name = "RoE by quartiles", labels = c("1st quartile", "2nd quartile", "3rd quartile", "4th quartile")) + 
  theme(axis.text.x = element_blank(),
        axis.title.x = element_blank(),
        axis.ticks.x = element_blank()) +
  facet_wrap(~ variable, scales = "free_x") +
  labs(y = "z-score", fill = "RoE by quartiles")

## Warning: Removed 187 rows containing non-finite values (stat_boxplot).

No need for z-score with scale free :)

data_stata_win %>%
  mutate(TA = log(TA),
         LoanstoTA = LoanstoTA*100,
         NonIntInc_pct = NonIntInc_pct*100,
         T1LeverageRatio = T1LeverageRatio*100,
         LoanLossProv_pct = LoanLossProv_pct*100,
         NonPerfLoans_pct = NonPerfLoans_pct*100,
         LongTermDebt_pct = LongTermDebt_pct*100,
         LtD = LtD*100,
         LeverageRatio = LeverageRatio*100,
         RoE_1 = if_else(RoE <= quantile(RoE, 0.25), 1, 0),
         RoE_2 = if_else(RoE > quantile(RoE, 0.25) & RoE <= quantile(RoE, 0.50), 1, 0),
         RoE_3 = if_else(RoE > quantile(RoE, 0.50) & RoE <= quantile(RoE, 0.75), 1, 0),
         RoE_4 = if_else(RoE > quantile(RoE, 0.75) & RoE <= quantile(RoE, 1), 1, 0),
         RoE_quartiles = if_else(RoE <= quantile(RoE, 0.25), 1, if_else(RoE <= quantile(RoE, 0.50), 2, if_else(RoE <= quantile(RoE, 0.75), 3, if_else(RoE <= quantile(RoE, 1), 4, 0)))),
         RoE_top_10 = if_else(RoE > quantile(RoE, 0.90), 1, 0),
         RoE_bottom_10 = if_else(RoE < quantile(RoE, 0.1), 1, 0),
         RoE_top_50 = if_else(RoE > quantile(RoE, 0.5), 1, 0)) %>%
  gather(key = "variable", value = "value", TA:LeverageRatio, T1_pct:GDP_pct) %>%
  filter(variable != "Inflation" & variable != "GDP_pct") %>%
  mutate(variable = as.factor(variable),
         variable = factor(variable, levels(variable)[c(10, 9, 12, 1, 7, 2, 11, 3, 8, 6, 4, 5)],
                           labels = c("RoE", "RoA", "ln(TA)", "Efficiency", "Non-interest income", "Leverage Ratio", "T1 (% RWAs)", "Loan Loss Provisions", "Non-performing Loans", "Loans to Deposits", "Loans to Total Assets", "Long-term Debt"))) %>%
  ggplot(aes(y = value, x = variable, fill = factor(RoE_quartiles))) +
  geom_boxplot(outlier.colour = "grey") +
  scale_fill_discrete(name = "RoE by quartiles", labels = c("1st quartile", "2nd quartile", "3rd quartile", "4th quartile")) + 
  theme(axis.text.x = element_blank(),
        axis.title.x = element_blank(),
        axis.ticks.x = element_blank(),
        axis.title.y = element_blank()) +
  facet_wrap(~ variable, scales = "free")

## Warning: Removed 187 rows containing non-finite values (stat_boxplot).

RoA

data_stata_win %>%
  mutate(TA = log(TA),
         LoanstoTA = LoanstoTA*100,
         NonIntInc_pct = NonIntInc_pct*100,
         T1LeverageRatio = T1LeverageRatio*100,
         LoanLossProv_pct = LoanLossProv_pct*100,
         NonPerfLoans_pct = NonPerfLoans_pct*100,
         LongTermDebt_pct = LongTermDebt_pct*100,
         LtD = LtD*100,
         LeverageRatio = LeverageRatio*100,
         RoA_1 = if_else(RoA <= quantile(RoA, 0.25), 1, 0),
         RoA_2 = if_else(RoA > quantile(RoA, 0.25) & RoA <= quantile(RoA, 0.50), 1, 0),
         RoA_3 = if_else(RoA > quantile(RoA, 0.50) & RoA <= quantile(RoA, 0.75), 1, 0),
         RoA_4 = if_else(RoA > quantile(RoA, 0.75) & RoA <= quantile(RoA, 1), 1, 0),
         RoA_quartiles = if_else(RoA <= quantile(RoA, 0.25), 1, if_else(RoA <= quantile(RoA, 0.50), 2, if_else(RoA <= quantile(RoA, 0.75), 3, if_else(RoA <= quantile(RoA, 1), 4, 0)))),
         RoA_top_10 = if_else(RoA > quantile(RoA, 0.90), 1, 0),
         RoA_bottom_10 = if_else(RoA < quantile(RoA, 0.1), 1, 0),
         RoA_top_50 = if_else(RoA > quantile(RoA, 0.5), 1, 0)) %>%
  gather(key = "variable", value = "value", TA:LeverageRatio, T1_pct:GDP_pct) %>%
  filter(variable != "Inflation" & variable != "GDP_pct") %>%
  mutate(variable = as.factor(variable),
         variable = factor(variable, levels(variable)[c(9, 10, 12, 1, 7, 2, 11, 3, 8, 6, 4, 5)],
                           labels = c("RoA", "RoE", "ln(TA)", "Efficiency", "Non-interest income", "Leverage Ratio", "T1 (% RWAs)", "Loan Loss Provisions", "Non-performing Loans", "Loans to Deposits", "Loans to Total Assets", "Long-term Debt"))) %>%
  ggplot(aes(y = value, x = variable, fill = factor(RoA_quartiles))) +
  geom_boxplot(outlier.colour = "grey") +
  scale_fill_discrete(name = "RoA by quartiles", labels = c("1st quartile", "2nd quartile", "3rd quartile", "4th quartile")) + 
  theme(axis.text.x = element_blank(),
        axis.title.x = element_blank(),
        axis.ticks.x = element_blank(),
        axis.title.y = element_blank()) +
  facet_wrap(~ variable, scales = "free")

## Warning: Removed 187 rows containing non-finite values (stat_boxplot).

Comparing impact of risk-weights

RoA_RW <- data_stata_win %>%
  mutate(TA = log(TA),
         LoanstoTA = LoanstoTA*100,
         NonIntInc_pct = NonIntInc_pct*100,
         T1LeverageRatio = T1LeverageRatio*100,
         LoanLossProv_pct = LoanLossProv_pct*100,
         NonPerfLoans_pct = NonPerfLoans_pct*100,
         LongTermDebt_pct = LongTermDebt_pct*100,
         LtD = LtD*100,
         LeverageRatio = LeverageRatio*100,
         RoA_1 = if_else(RoA <= quantile(RoA, 0.25), 1, 0),
         RoA_2 = if_else(RoA > quantile(RoA, 0.25) & RoA <= quantile(RoA, 0.50), 1, 0),
         RoA_3 = if_else(RoA > quantile(RoA, 0.50) & RoA <= quantile(RoA, 0.75), 1, 0),
         RoA_4 = if_else(RoA > quantile(RoA, 0.75) & RoA <= quantile(RoA, 1), 1, 0),
         RoA_quartiles = if_else(RoA <= quantile(RoA, 0.25), 1, if_else(RoA <= quantile(RoA, 0.50), 2, if_else(RoA <= quantile(RoA, 0.75), 3, if_else(RoA <= quantile(RoA, 1), 4, 0)))),
         RoA_top_10 = if_else(RoA > quantile(RoA, 0.90), 1, 0),
         RoA_bottom_10 = if_else(RoA < quantile(RoA, 0.1), 1, 0),
         RoA_top_50 = if_else(RoA > quantile(RoA, 0.5), 1, 0)) %>%
  gather(key = "variable", value = "value", est_RW) %>%
  filter(variable != "Inflation" & variable != "GDP_pct") %>%
  ggplot(aes(y = value, x = variable, fill = factor(RoA_quartiles))) +
  geom_boxplot(outlier.colour = "grey") +
  scale_fill_discrete(name = "RoA by quartiles", labels = c("1st quartile", "2nd quartile", "3rd quartile", "4th quartile")) + 
  theme(axis.text.x = element_blank(),
        axis.title.x = element_blank(),
        axis.ticks.x = element_blank(),
        axis.title.y = element_blank()) +
  facet_wrap(~ variable, scales = "free")

RoE_RW <- data_stata_win %>%
  mutate(TA = log(TA),
         LoanstoTA = LoanstoTA*100,
         NonIntInc_pct = NonIntInc_pct*100,
         T1LeverageRatio = T1LeverageRatio*100,
         LoanLossProv_pct = LoanLossProv_pct*100,
         NonPerfLoans_pct = NonPerfLoans_pct*100,
         LongTermDebt_pct = LongTermDebt_pct*100,
         LtD = LtD*100,
         LeverageRatio = LeverageRatio*100,
         RoE_1 = if_else(RoE <= quantile(RoE, 0.25), 1, 0),
         RoE_2 = if_else(RoE > quantile(RoE, 0.25) & RoE <= quantile(RoE, 0.50), 1, 0),
         RoE_3 = if_else(RoE > quantile(RoE, 0.50) & RoE <= quantile(RoE, 0.75), 1, 0),
         RoE_4 = if_else(RoE > quantile(RoE, 0.75) & RoE <= quantile(RoE, 1), 1, 0),
         RoE_quartiles = if_else(RoE <= quantile(RoE, 0.25), 1, if_else(RoE <= quantile(RoE, 0.50), 2, if_else(RoE <= quantile(RoE, 0.75), 3, if_else(RoE <= quantile(RoE, 1), 4, 0)))),
         RoE_top_10 = if_else(RoE > quantile(RoE, 0.90), 1, 0),
         RoE_bottom_10 = if_else(RoE < quantile(RoE, 0.1), 1, 0),
         RoE_top_50 = if_else(RoE > quantile(RoE, 0.5), 1, 0)) %>%
  gather(key = "variable", value = "value", est_RW) %>%
  filter(variable != "Inflation" & variable != "GDP_pct") %>%
  ggplot(aes(y = value, x = variable, fill = factor(RoE_quartiles))) +
  geom_boxplot(outlier.colour = "grey") +
  scale_fill_discrete(name = "RoE by quartiles", labels = c("1st quartile", "2nd quartile", "3rd quartile", "4th quartile")) + 
  theme(axis.text.x = element_blank(),
        axis.title.x = element_blank(),
        axis.ticks.x = element_blank(),
        axis.title.y = element_blank()) +
  facet_wrap(~ variable, scales = "free")

grid.arrange(RoE_RW, RoA_RW, ncol=2)

## Warning: Removed 61 rows containing non-finite values (stat_boxplot).

## Warning: Removed 61 rows containing non-finite values (stat_boxplot).

top 10% RoE

data_stata_z_gather %>%
  filter(variable != "Inflation" & variable != "GDP_pct" & variable != "T1LeverageRatio") %>%
  mutate(variable = as.factor(variable),
         variable = factor(variable, levels(variable)[c(11, 10, 13, 3, 12, 4, 9, 7, 5, 6, 8, 1, 2)])) %>%
  ggplot(aes(y = value, x = variable, fill = factor(RoE_top_10))) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5),
        axis.title.x = element_blank())  +
  labs(y = "z-score", fill = "RoE in top 10%")

## Warning: Removed 248 rows containing non-finite values (stat_boxplot).

bottom 10% RoE

data_stata_z_gather %>%
  filter(variable != "Inflation" & variable != "GDP_pct" & variable != "T1LeverageRatio") %>%
  mutate(variable = as.factor(variable),
         variable = factor(variable, levels(variable)[c(11, 10, 13, 3, 12, 4, 9, 7, 5, 6, 8, 1, 2)])) %>%
  ggplot(aes(y = value, x = variable, fill = factor(RoE_bottom_10))) +
  geom_boxplot() +
  theme(axis.text.x = element_blank(),
        axis.title.x = element_blank(),
        axis.ticks.x = element_blank())  +
  labs(y = "z-score", fill = "RoE in bottom 10%") +
  facet_wrap(~variable, scales ="free_x")

## Warning: Removed 248 rows containing non-finite values (stat_boxplot).

data_stata_z_gather %>%
  mutate(RoE_top_50 = factor(RoE_top_50)) %>%
  select(id, Year, variable, value, RoE_top_50) %>%
  spread(key = variable, value = value) %>%
  select(1:5, 8:14, 17:18, 15:16) %>%
  ggparcoord(alpha = .1,
             scale = "center",
             columns = 4:16,
             groupColumn = "RoE_top_50")

data_stata_z_gather %>%
  filter(Year == 2010) %>%
  mutate(RoE_4 = factor(RoE_4)) %>%
  select(id, Year, variable, value, RoE_4) %>%
  spread(key = variable, value = value) %>%
  select(1:5, 8:14, 17, 15:16) %>%
  ggparcoord(alpha = .3,
             scale = "center",
             columns = 4:15,
             groupColumn = "RoE_4")

examples of outliers

Loans to Deposits

Original

data_select %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = LtD)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

vs Winsorised

data_stata_win %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = LtD)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

data_stata_z_year_win %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = LtD)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

Efficiency

Original

data_select %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = Efficiency)) +
  geom_point() +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

vs Winsorised

data_stata_win %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = Efficiency)) +
  geom_jitter(width = 0.5, height = 0.5) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

vs Z-score by year winsorised

data_stata_z_year_win %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = Efficiency)) +
  geom_jitter(width = 0.5, height = 0.5) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

Leverage Ratio

Original

data_select %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = LeverageRatio)) +
  geom_point() +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

vs Winsorised

data_stata_win %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = LeverageRatio)) +
  geom_point() +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

vs Z-score by year winsorised

data_stata_z_year_win %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = LeverageRatio)) +
  geom_point() +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

Loan Loss provision

Original

data_select %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = LoanLossProv_pct)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

vs Winsorised

data_stata_win %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = LoanLossProv_pct)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

Z-score by year winsorised

data_stata_z_year_win %>%
  #filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = LoanLossProv_pct)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

Non-performing loans

data_select %>%
  filter(Year == 2010) %>%
  ggplot(aes(y = RoE, x = NonPerfLoans_pct)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

## Warning: Removed 21 rows containing non-finite values (stat_smooth).

## Warning: Removed 21 rows containing missing values (geom_point).

Non-interest income

data_select %>%
  filter(Year == 2018) %>%
  ggplot(aes(y = RoE, x = NonIntInc_pct)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

Non-interest income

data_stata_win %>%
  ggplot(aes(y = RoE, x = NonIntInc_pct)) +
  geom_point() +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

data_stata_z_year_win %>%
  ggplot(aes(y = RoE, x = NonIntInc_pct)) +
  geom_point() +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

98th percentile vs Z-score winsorisation

data_stata %>%
  ggplot(aes(x = LeverageRatio)) +
  geom_histogram(bins = 100, alpha = 0.5,) +
  geom_histogram(data = data_stata_win, fill = "green", alpha = 0.2, bins = 100) +
  geom_histogram(data = data_stata_z_win, fill = "red", alpha = 0.2, bins = 100) +
  scale_x_continuous(labels = percent_format()) +
  #geom_vline(xintercept = 1) +
  #geom_vline(data = data_stata_win %>% group_by(Year) %>% summarise(median = median((T1_pct/100)/LeverageRatio, na.rm = TRUE)), aes(xintercept = median), linetype = "dashed", col = "red") +
  labs()

data_stata %>%
  ggplot(aes(x = LoanLossProv_pct)) +
  geom_histogram(bins = 100, alpha = 0.3) +
  geom_histogram(data = data_stata_win, fill = "green", alpha = 0.3, bins = 100) +
  geom_histogram(data = data_stata_z_win, fill = "red", alpha = 0.3, bins = 100) +
  scale_x_continuous(labels = percent_format()) +
  #geom_vline(xintercept = 1) +
  #geom_vline(data = data_stata_win %>% group_by(Year) %>% summarise(median = median((T1_pct/100)/LeverageRatio, na.rm = TRUE)), aes(xintercept = median), linetype = "dashed", col = "red") +
  labs() +
  facet_wrap(~ Year)

data_stata %>%
  ggplot(aes(x = LtD)) +
  geom_histogram(bins = 100, alpha = 0.5,) +
  geom_histogram(data = data_stata_win, fill = "green", alpha = 0.2, bins = 100) +
  geom_histogram(data = data_stata_z_win, fill = "red", alpha = 0.2, bins = 100) +
  scale_x_continuous(labels = percent_format()) +
  #geom_vline(xintercept = 1) +
  #geom_vline(data = data_stata_win %>% group_by(Year) %>% summarise(median = median((T1_pct/100)/LeverageRatio, na.rm = TRUE)), aes(xintercept = median), linetype = "dashed", col = "red") +
  labs()

data_stata %>%
  ggplot(aes(x = NonIntInc_pct)) +
  geom_histogram(bins = 100, alpha = 0.5,) +
  geom_histogram(data = data_stata_win, fill = "green", alpha = 0.2, bins = 100) +
  geom_histogram(data = data_stata_z_win, fill = "red", alpha = 0.2, bins = 100) +
  scale_x_continuous(labels = percent_format()) +
  #geom_vline(xintercept = 1) +
  #geom_vline(data = data_stata_win %>% group_by(Year) %>% summarise(median = median((T1_pct/100)/LeverageRatio, na.rm = TRUE)), aes(xintercept = median), linetype = "dashed", col = "red") +
  labs()

data_stata %>%
  ggplot(aes(x = Efficiency)) +
  geom_histogram(bins = 100, alpha = 0.5,) +
  geom_histogram(data = data_stata_win, fill = "green", alpha = 0.2, bins = 100) +
  geom_histogram(data = data_stata_z_win, fill = "red", alpha = 0.2, bins = 100) +
  #geom_vline(xintercept = 1) +
  #geom_vline(data = data_stata_win %>% group_by(Year) %>% summarise(median = median((T1_pct/100)/LeverageRatio, na.rm = TRUE)), aes(xintercept = median), linetype = "dashed", col = "red") +
  labs()

Examining correlated metrics

LR and T1_pct

data_stata_win %>%
  #filter(Year == 2017) %>%
  ggplot(aes(y = LeverageRatio, x = T1_pct/100)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  scale_y_continuous(labels = percent_format()) +
  geom_abline(intercept = 0, linetype = "dashed") +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  labs(x = "T1 as % of RWAs", y = "Leverage Ratio") +
  facet_wrap(~ Year)

## Warning: Removed 61 rows containing non-finite values (stat_smooth).

## Warning: Removed 61 rows containing missing values (geom_point).

T1 as % of RWAs was around 125% of the Leverage Ratio, but has been falling in the recent years to around 105% of LR. Not sure if T1_pct is falling or LR increasing.

data_stata_win %>%
  ggplot(aes(x = (T1_pct/100)/LeverageRatio)) +
  geom_histogram() +
  scale_x_continuous(labels = percent_format()) +
  geom_vline(xintercept = 1) +
  geom_vline(data = data_stata_win %>% group_by(Year) %>% summarise(median = median((T1_pct/100)/LeverageRatio, na.rm = TRUE)), aes(xintercept = median), linetype = "dashed", col = "red") +
  labs(x = "T1 RWCR as percent of Leverage Ratio") +
  facet_wrap(~ Year)

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Warning: Removed 61 rows containing non-finite values (stat_bin).

Convergence mainlu due to fall in T1 as % of RWAs, but LR increased as well.

=> also evidence RW has increased. Requiring a higher LR for the same T1 RWC

data_stata_win %>%
  mutate(T1_pct = T1_pct/100) %>%
  gather(key = "capital_ratio", value = "value", T1_pct, LeverageRatio) %>%
  ggplot(aes(x = value, fill = capital_ratio)) +
  geom_histogram(alpha = 0.5, position="identity") +
  geom_vline(data = data_stata_win %>% group_by(Year) %>% summarise(T1_median = median(T1_pct, na.rm = TRUE)/100), aes(xintercept = T1_median), linetype = "dashed", col = "green") +
  geom_vline(data = data_stata_win %>% group_by(Year) %>% summarise(LR_median = median(LeverageRatio, na.rm = TRUE)), aes(xintercept = LR_median), linetype = "dashed", col = "red") +
  scale_x_continuous(labels = percent_format()) +
  labs(x = "Capital ratio") +
  facet_wrap(~ Year)

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Warning: Removed 61 rows containing non-finite values (stat_bin).

data_stata_lag %>%
  ggplot(aes(x = LeverageRatio, y = RoE)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

LR and TA

data_stata_win %>%
  #filter(Year == 2017) %>%
  ggplot(aes(y = LeverageRatio, x = TA)) +
  geom_point() +
  scale_x_log10() +
  scale_y_continuous(labels = percent_format()) +
  geom_abline(intercept = 0, linetype = "dashed") +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  labs(y = "Leverage Ratio") +
  facet_wrap(~ Year)

#### t-test LR by size

Capital adequacy

t.test(LeverageRatio ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  LeverageRatio by TA_large
## t = -6.2241, df = 1316.3, p-value = 6.496e-10
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.9820569 -0.5113536
## sample estimates:
## mean in group 0 mean in group 1 
##        10.94597        11.69268

t.test(T1_pct ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  T1_pct by TA_large
## t = 4.9144, df = 1209.4, p-value = 1.013e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.526345 1.225857
## sample estimates:
## mean in group 0 mean in group 1 
##        14.00539        13.12929

mean(data_stata_reg$T1LeverageRatio/data_stata_reg$LeverageRatio, na.rm = TRUE)

## [1] 0.8580176

t.test(est_RW ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  est_RW by TA_large
## t = -4.8845, df = 1262.8, p-value = 1.169e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -5.048775 -2.155303
## sample estimates:
## mean in group 0 mean in group 1 
##        70.45544        74.05748

Liquidity

t.test(LtD ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  LtD by TA_large
## t = -1.2039, df = 1116.5, p-value = 0.2289
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.8120345  0.9129405
## sample estimates:
## mean in group 0 mean in group 1 
##        86.00560        87.45514

t.test(LoanstoTA ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  LoanstoTA by TA_large
## t = 4.8202, df = 1319.1, p-value = 1.6e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.841901 4.370092
## sample estimates:
## mean in group 0 mean in group 1 
##        67.50749        64.40149

t.test(LongTermDebt_pct ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  LongTermDebt_pct by TA_large
## t = -8.3443, df = 856.57, p-value = 2.852e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -2.799343 -1.733200
## sample estimates:
## mean in group 0 mean in group 1 
##        1.895836        4.162108

Profitability

t.test(RoE ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  RoE by TA_large
## t = -0.93048, df = 1068.2, p-value = 0.3523
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1.059779  0.377982
## sample estimates:
## mean in group 0 mean in group 1 
##        8.265548        8.606446

t.test(RoA ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  RoA by TA_large
## t = -2.0189, df = 1264.4, p-value = 0.04371
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.117965710 -0.001691377
## sample estimates:
## mean in group 0 mean in group 1 
##       0.9199078       0.9797364

Other

t.test(Efficiency ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  Efficiency by TA_large
## t = 3.3866, df = 1329.9, p-value = 0.0007284
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.9328889 3.5017549
## sample estimates:
## mean in group 0 mean in group 1 
##        64.54761        62.33028

t.test(LoanLossProv_pct ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  LoanLossProv_pct by TA_large
## t = -2.3501, df = 1325.4, p-value = 0.01892
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.18380280 -0.01655334
## sample estimates:
## mean in group 0 mean in group 1 
##       0.4056432       0.5058213

t.test(NonIntInc_pct ~ TA_large, data = data_stata_reg)

## 
##  Welch Two Sample t-test
## 
## data:  NonIntInc_pct by TA_large
## t = -7.9598, df = 1230.9, p-value = 3.886e-15
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -6.081063 -3.676156
## sample estimates:
## mean in group 0 mean in group 1 
##        20.48502        25.36363

LtD and Loans to TA

data_select %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = LtD, x = LoanstoTA)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  scale_y_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

data_select %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = RoE, x = LoanstoTA)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

data_select %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = RoE, x = LtD)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

data_select %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = RoE, x = -5.7*LtD + 7.1*LoanstoTA)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

data_select %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = RoE, x = LoanstoTA/LtD)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  labs(x = "Deposits to TA") + 
  facet_wrap(~ Year)

debt to RoE

data_select %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = RoE, x = LongTermDebt_pct)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  labs() + 
  facet_wrap(~ Year)

longterm debt to deposits

data_select %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = LongTermDebt_pct, x = LoanstoTA/LtD)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  scale_y_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  labs(x = "Deposits to TA") + 
  facet_wrap(~ Year)

NonIntIncome and Loans to TA

data_select %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = NonIntInc_pct, x = LoanstoTA)) +
  geom_point() +
  scale_x_continuous(labels = percent_format()) +
  scale_y_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  facet_wrap(~ Year)

Testing impact of Deposits from regression without deposits

data_select %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = -5.74*LtD + 7.18*LoanstoTA, x = LoanstoTA/LtD)) +
  geom_point() +
  geom_abline(intercept = -4, slope = 4.9, color="red",
              linetype="dashed", size=1.5) +
  scale_x_continuous(labels = percent_format()) +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  labs(x = "Deposits to TA") + 
  facet_wrap(~ Year)

data_stata %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = RoE, x = -5.74*LtD + 7.18*LoanstoTA + 17.39*LongTermDebt_pct - .2436*Efficiency - 421*LoanLossProv_pct - .77*log(TA) + 0.075*T1_pct + 37.9 + 0.65*Inflation + .71*GDP_pct + 23*Outlier_pos - 23.4*Outlier_neg)) +
  geom_point() +
  geom_abline(xintercept = 0, linetype = "dashed") +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  labs() + 
  facet_wrap(~ Year)

## Warning: Ignoring unknown parameters: xintercept

## Warning: Removed 4 rows containing non-finite values (stat_smooth).

## Warning: Removed 4 rows containing missing values (geom_point).

data_select %>%
  filter(Year == 2017) %>%
  ggplot(aes(y = RoE, x = .09*LtD -2.1*LoanstoTA + 17.39*LongTermDebt_pct - .328*Efficiency - 537*LoanLossProv_pct - 1.73*log(TA) + 0.14*T1_pct + 66.8 + 8.1*NonIntInc_pct + 0.60*Inflation + .55*GDP_pct)) +
  geom_point() +
  geom_abline(xintercept = 0, linetype = "dashed") +
  stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
  labs() + 
  facet_wrap(~ Year)

Average Bank will have summary_2018$mean_LtD*-5.74 + summary_2018$mean_LoanstoTA*7.18 pp change in RoE (due to LtD and LtTA)

A bank with a high loan ratio LtD = 1 and LtTA = 0.8 (deposits = 0.8/1) will have 1*-5.74 + 0.8*7.18 pp change in RoE

A bank with a low deposit ratio LtD = 2 and LtTA = 0.8 (deposits = 0.8/2) will have 2*-5.74 + 0.8*7.18 pp change in RoE

data_stata_changes %>%
  ggplot(aes(x = TA)) +
  geom_histogram()

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Fixed or Random effects charts

Looking at 14 “random” samples

LtD

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 1) %>%
  ggplot(aes(x = LtD, y = RoE, group = Bank, col = Bank)) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 1) %>%
  ggplot(aes(x = LtD, y = RoE, group = factor(Year), col = factor(Year))) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

TA

-> very different for individual vs agreggate

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 1) %>%
  ggplot(aes(x = TA, y = RoE, group = Bank, col = Bank)) +
  geom_point() +
  scale_x_log10() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 1) %>%
  ggplot(aes(x = TA, y = RoE, group = factor(Year), col = factor(Year))) +
  geom_point() +
  scale_x_log10() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

Efficiency

-> similar for individual and aggregate

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 3) %>%
  ggplot(aes(x = Efficiency, y = RoE, group = Bank, col = Bank)) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

With increasing Efficiency the gap between real RoE and epxected RoE increases as Efficiency hasn’t been taking into consideration yet.

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 5) %>%
  ggplot(aes(x = Efficiency, y = RoE- (40.61+(-0.564*log(TA)-0.0240*LtD+0.0788*NonIntInc_pct-0.262*LeverageRatio-3.942*LoanLossProv_pct+0.571*Inflation+0.721*GDP_pct)), group = Bank, col = Bank)) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2)

#+  scale_y_continuous(limits = c(-30, 50))

data_stata_win_reg %>%
  mutate(id = as.integer(id)) %>%
  left_join(random, by = c("id")) %>%
  filter(random == 4) %>%
  ggplot(aes(y = RoE, x = -10+40.61+(-0.564*log(TA)-0.0240*LtD-0.256*Efficiency+0.0788*NonIntInc_pct-0.262*LeverageRatio-3.942*LoanLossProv_pct+0.571*Inflation+0.721*GDP_pct), group = Bank, col = Bank)) +
  geom_point() +
  geom_abline(intercept = 0, linetype = "dashed") +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2)

#+  scale_y_continuous(limits = c(-30, 50))

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 1) %>%
  ggplot(aes(x = Efficiency, y = RoE, group = factor(Year), col = factor(Year))) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

T1_pct

-> mixed impact some increasing, some falling

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 4) %>%
  ggplot(aes(x = T1_pct, y = RoE, group = Bank, col = Bank)) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random < 10) %>%
  ggplot(aes(x = T1_pct, y = RoE, group = Bank, col = Bank)) +
  geom_point(alpha = 0.5, size = 0.5) +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 1) +
  scale_y_continuous(limits = c(0, 30)) +
  facet_wrap(~ random) +
  theme(legend.position = "none")

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 1) %>%
  ggplot(aes(x = T1_pct, y = RoE, group = factor(Year), col = factor(Year))) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

leverag Ratio

-> mixed impact some increasing, some falling

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 1) %>%
  ggplot(aes(x = LeverageRatio, y = RoE, group = Bank, col = Bank)) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

Loan loss provisions

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 3) %>%
  ggplot(aes(x = LoanLossProv_pct, y = RoE, group = Bank, col = Bank)) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 3) %>%
  ggplot(aes(x = LoanLossProv_pct, y = RoE, group = factor(Year), col = factor(Year))) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

% non-interest income

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 3) %>%
  ggplot(aes(x = NonIntInc_pct, y = RoE, group = Bank, col = Bank)) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

Each year the level is different, but relationship the same

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 1) %>%
  ggplot(aes(x = NonIntInc_pct, y = RoE, group = factor(Year), col = factor(Year))) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

% long-term debt

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 1) %>%
  ggplot(aes(x = LongTermDebt_pct, y = RoE, group = Bank, col = Bank)) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

data_stata_win %>%
  left_join(random, by = c("id")) %>%
  filter(random == 1) %>%
  ggplot(aes(x = LongTermDebt_pct, y = RoE, group = factor(Year), col = factor(Year))) +
  geom_point() +
  geom_smooth(method = "lm", linetype = "dashed", se = FALSE) +
  geom_smooth(aes(group = 1), method = "lm", linetype = "dashed", se = FALSE, colour = "black", size = 2) +
  scale_y_continuous(limits = c(0, 30))

Subset selection

ROE

subset_selection <- regsubsets(RoE~., data = data_stata_win_sub %>% select(-RoA), nvmax = 12)

## Reordering variables and trying again:

summary(subset_selection)

## Subset selection object
## Call: regsubsets.formula(RoE ~ ., data = data_stata_win_sub %>% select(-RoA), 
##     nvmax = 12)
## 22 Variables  (and intercept)
##                  Forced in Forced out
## TA                   FALSE      FALSE
## LtD                  FALSE      FALSE
## LoanstoTA            FALSE      FALSE
## NonIntInc_pct        FALSE      FALSE
## Efficiency           FALSE      FALSE
## LeverageRatio        FALSE      FALSE
## T1_pct               FALSE      FALSE
## LoanLossProv_pct     FALSE      FALSE
## NonPerfLoans_pct     FALSE      FALSE
## LongTermDebt_pct     FALSE      FALSE
## Inflation            FALSE      FALSE
## GDP_pct              FALSE      FALSE
## est_T1LR             FALSE      FALSE
## est_RW               FALSE      FALSE
## FED_rate             FALSE      FALSE
## TA_large             FALSE      FALSE
## TA_1                 FALSE      FALSE
## TA_2                 FALSE      FALSE
## TA_3                 FALSE      FALSE
## TA_4                 FALSE      FALSE
## TA_5                 FALSE      FALSE
## TA_small             FALSE      FALSE
## 1 subsets of each size up to 13
## Selection Algorithm: exhaustive
##           TA  LtD LoanstoTA NonIntInc_pct Efficiency LeverageRatio T1_pct
## 1  ( 1 )  " " " " " "       " "           " "        " "           " "   
## 2  ( 1 )  " " " " " "       " "           "*"        " "           " "   
## 3  ( 1 )  " " " " " "       "*"           "*"        " "           " "   
## 4  ( 1 )  " " " " " "       "*"           "*"        "*"           " "   
## 5  ( 1 )  " " " " " "       "*"           "*"        "*"           " "   
## 6  ( 1 )  " " "*" " "       "*"           "*"        "*"           " "   
## 7  ( 1 )  " " "*" " "       "*"           "*"        "*"           " "   
## 8  ( 1 )  " " "*" " "       "*"           "*"        "*"           " "   
## 9  ( 1 )  " " "*" " "       "*"           "*"        "*"           " "   
## 10  ( 1 ) " " "*" " "       "*"           "*"        "*"           " "   
## 11  ( 1 ) " " "*" " "       "*"           "*"        "*"           " "   
## 12  ( 1 ) " " "*" " "       "*"           "*"        "*"           " "   
## 13  ( 1 ) " " "*" " "       "*"           "*"        "*"           " "   
##           LoanLossProv_pct NonPerfLoans_pct LongTermDebt_pct Inflation GDP_pct
## 1  ( 1 )  "*"              " "              " "              " "       " "    
## 2  ( 1 )  "*"              " "              " "              " "       " "    
## 3  ( 1 )  "*"              " "              " "              " "       " "    
## 4  ( 1 )  "*"              " "              " "              " "       " "    
## 5  ( 1 )  "*"              " "              " "              " "       " "    
## 6  ( 1 )  "*"              " "              " "              " "       " "    
## 7  ( 1 )  "*"              " "              "*"              " "       " "    
## 8  ( 1 )  "*"              " "              "*"              " "       " "    
## 9  ( 1 )  "*"              " "              "*"              " "       " "    
## 10  ( 1 ) "*"              " "              "*"              "*"       "*"    
## 11  ( 1 ) "*"              " "              "*"              "*"       "*"    
## 12  ( 1 ) "*"              "*"              "*"              "*"       "*"    
## 13  ( 1 ) "*"              "*"              "*"              "*"       "*"    
##           est_T1LR est_RW FED_rate TA_large TA_small TA_1 TA_2 TA_3 TA_4 TA_5
## 1  ( 1 )  " "      " "    " "      " "      " "      " "  " "  " "  " "  " " 
## 2  ( 1 )  " "      " "    " "      " "      " "      " "  " "  " "  " "  " " 
## 3  ( 1 )  " "      " "    " "      " "      " "      " "  " "  " "  " "  " " 
## 4  ( 1 )  " "      " "    " "      " "      " "      " "  " "  " "  " "  " " 
## 5  ( 1 )  " "      " "    "*"      " "      " "      " "  " "  " "  " "  " " 
## 6  ( 1 )  " "      " "    "*"      " "      " "      " "  " "  " "  " "  " " 
## 7  ( 1 )  " "      " "    "*"      " "      " "      " "  " "  " "  " "  " " 
## 8  ( 1 )  " "      " "    "*"      " "      " "      " "  " "  " "  " "  "*" 
## 9  ( 1 )  " "      " "    "*"      " "      " "      " "  " "  " "  "*"  "*" 
## 10  ( 1 ) " "      "*"    " "      " "      " "      " "  " "  " "  " "  "*" 
## 11  ( 1 ) " "      "*"    " "      " "      " "      " "  " "  " "  "*"  "*" 
## 12  ( 1 ) " "      "*"    " "      " "      " "      " "  " "  " "  "*"  "*" 
## 13  ( 1 ) " "      "*"    " "      " "      " "      " "  "*"  " "  "*"  "*"

res.sum <- summary(subset_selection)
data.frame(
  Adj.R2 = which.max(res.sum$adjr2),
  CP = which.min(res.sum$cp),
  BIC = which.min(res.sum$bic)
)

subset_selection2 <- lm(RoE ~ TA + LtD + LoanstoTA + Efficiency + T1_pct + LeverageRatio + LoanLossProv_pct + NonPerfLoans_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_sub %>% select(-RoA))
ols_step_forward_p(subset_selection2)

## 
##                                  Selection Summary                                   
## ------------------------------------------------------------------------------------
##         Variable                          Adj.                                          
## Step        Entered         R-Square    R-Square      C(p)          AIC        RMSE     
## ------------------------------------------------------------------------------------
##    1    LoanLossProv_pct      0.3205      0.3200    1521.8888    7418.0950    3.9123    
##    2    Efficiency            0.5557      0.5550     537.6086    6854.3076    3.1649    
##    3    NonIntInc_pct         0.6137      0.6128     296.1160    6669.8051    2.9520    
##    4    LeverageRatio         0.6566      0.6555     118.3492    6515.1456    2.7845    
##    5    LtD                   0.6628      0.6615      94.3897    6492.9200    2.7603    
##    6    Inflation             0.6679      0.6664      74.6645    6474.3016    2.7401    
##    7    GDP_pct               0.6732      0.6714      54.7197    6455.1455    2.7194    
##    8    LongTermDebt_pct      0.6761      0.6742      44.3069    6445.0284    2.7081    
##    9    TA                    0.6790      0.6768      34.3720    6435.2729    2.6972    
##   10    NonPerfLoans_pct      0.6818      0.6791       6.8422    5802.4154    2.6680    
## ------------------------------------------------------------------------------------

RoA

subset_selection_RoA <- regsubsets(RoA~., data = data_stata_win_sub %>% select(-RoE), nvmax = 12)

## Reordering variables and trying again:

summary(subset_selection_RoA)

## Subset selection object
## Call: regsubsets.formula(RoA ~ ., data = data_stata_win_sub %>% select(-RoE), 
##     nvmax = 12)
## 22 Variables  (and intercept)
##                  Forced in Forced out
## TA                   FALSE      FALSE
## LtD                  FALSE      FALSE
## LoanstoTA            FALSE      FALSE
## NonIntInc_pct        FALSE      FALSE
## Efficiency           FALSE      FALSE
## LeverageRatio        FALSE      FALSE
## T1_pct               FALSE      FALSE
## LoanLossProv_pct     FALSE      FALSE
## NonPerfLoans_pct     FALSE      FALSE
## LongTermDebt_pct     FALSE      FALSE
## Inflation            FALSE      FALSE
## GDP_pct              FALSE      FALSE
## est_T1LR             FALSE      FALSE
## est_RW               FALSE      FALSE
## FED_rate             FALSE      FALSE
## TA_large             FALSE      FALSE
## TA_1                 FALSE      FALSE
## TA_2                 FALSE      FALSE
## TA_3                 FALSE      FALSE
## TA_4                 FALSE      FALSE
## TA_5                 FALSE      FALSE
## TA_small             FALSE      FALSE
## 1 subsets of each size up to 13
## Selection Algorithm: exhaustive
##           TA  LtD LoanstoTA NonIntInc_pct Efficiency LeverageRatio T1_pct
## 1  ( 1 )  " " " " " "       " "           "*"        " "           " "   
## 2  ( 1 )  " " " " " "       " "           "*"        " "           " "   
## 3  ( 1 )  " " " " " "       "*"           "*"        " "           " "   
## 4  ( 1 )  " " " " " "       "*"           "*"        " "           " "   
## 5  ( 1 )  " " "*" " "       "*"           "*"        " "           " "   
## 6  ( 1 )  " " "*" " "       "*"           "*"        " "           " "   
## 7  ( 1 )  " " " " "*"       "*"           "*"        " "           " "   
## 8  ( 1 )  " " "*" " "       "*"           "*"        " "           " "   
## 9  ( 1 )  " " "*" " "       "*"           "*"        "*"           " "   
## 10  ( 1 ) " " "*" " "       "*"           "*"        "*"           " "   
## 11  ( 1 ) " " "*" " "       "*"           "*"        "*"           " "   
## 12  ( 1 ) " " "*" " "       "*"           "*"        "*"           " "   
## 13  ( 1 ) " " "*" " "       "*"           "*"        "*"           " "   
##           LoanLossProv_pct NonPerfLoans_pct LongTermDebt_pct Inflation GDP_pct
## 1  ( 1 )  " "              " "              " "              " "       " "    
## 2  ( 1 )  "*"              " "              " "              " "       " "    
## 3  ( 1 )  "*"              " "              " "              " "       " "    
## 4  ( 1 )  "*"              " "              " "              " "       " "    
## 5  ( 1 )  "*"              " "              " "              " "       " "    
## 6  ( 1 )  "*"              " "              " "              " "       " "    
## 7  ( 1 )  "*"              " "              " "              " "       " "    
## 8  ( 1 )  "*"              " "              "*"              " "       " "    
## 9  ( 1 )  "*"              " "              "*"              " "       " "    
## 10  ( 1 ) "*"              " "              "*"              " "       " "    
## 11  ( 1 ) "*"              " "              "*"              " "       " "    
## 12  ( 1 ) "*"              " "              "*"              "*"       "*"    
## 13  ( 1 ) "*"              " "              "*"              "*"       "*"    
##           est_T1LR est_RW FED_rate TA_large TA_small TA_1 TA_2 TA_3 TA_4 TA_5
## 1  ( 1 )  " "      " "    " "      " "      " "      " "  " "  " "  " "  " " 
## 2  ( 1 )  " "      " "    " "      " "      " "      " "  " "  " "  " "  " " 
## 3  ( 1 )  " "      " "    " "      " "      " "      " "  " "  " "  " "  " " 
## 4  ( 1 )  " "      " "    "*"      " "      " "      " "  " "  " "  " "  " " 
## 5  ( 1 )  " "      " "    "*"      " "      " "      " "  " "  " "  " "  " " 
## 6  ( 1 )  " "      "*"    "*"      " "      " "      " "  " "  " "  " "  " " 
## 7  ( 1 )  " "      "*"    "*"      " "      " "      " "  " "  " "  " "  "*" 
## 8  ( 1 )  " "      "*"    "*"      " "      " "      " "  " "  " "  " "  "*" 
## 9  ( 1 )  " "      "*"    "*"      " "      " "      " "  " "  " "  " "  "*" 
## 10  ( 1 ) " "      "*"    "*"      " "      " "      " "  " "  " "  "*"  "*" 
## 11  ( 1 ) "*"      "*"    "*"      " "      " "      " "  " "  " "  "*"  "*" 
## 12  ( 1 ) " "      "*"    "*"      " "      " "      " "  " "  " "  "*"  "*" 
## 13  ( 1 ) "*"      "*"    "*"      " "      " "      " "  " "  " "  "*"  "*"

res.sum_RoA <- summary(subset_selection_RoA)
data.frame(
  Adj.R2 = which.max(res.sum$adjr2),
  CP = which.min(res.sum$cp),
  BIC = which.min(res.sum$bic)
)

subset_selection2_RoA <- lm(RoA ~ TA + LtD + LoanstoTA + Efficiency + T1_pct + LeverageRatio + LoanLossProv_pct + NonPerfLoans_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_sub %>% select(-RoE))
ols_step_forward_p(subset_selection2_RoA)

## 
##                                  Selection Summary                                   
## ------------------------------------------------------------------------------------
##         Variable                          Adj.                                          
## Step        Entered         R-Square    R-Square      C(p)          AIC        RMSE     
## ------------------------------------------------------------------------------------
##    1    Efficiency            0.3434      0.3429    1623.9666    1225.4920    0.3827    
##    2    LoanLossProv_pct      0.6028      0.6022     459.6630     557.9198    0.2978    
##    3    NonIntInc_pct         0.6589      0.6581     209.7312     357.3408    0.2761    
##    4    LeverageRatio         0.6697      0.6687     163.0751     316.3997    0.2718    
##    5    LtD                   0.6764      0.6751     135.1215     291.2589    0.2691    
##    6    T1_pct                0.6880      0.6866     105.8233     256.8532    0.2668    
##    7    GDP_pct               0.6931      0.6914      85.9046     238.2452    0.2647    
##    8    Inflation             0.6991      0.6972      61.3270     214.8002    0.2622    
##    9    TA                    0.7012      0.6990      54.4372     208.1741    0.2614    
##   10    LongTermDebt_pct      0.7056      0.7032      37.3207     191.4243    0.2596    
##   11    NonPerfLoans_pct      0.7001      0.6974      12.1277     158.1214    0.2569    
##   12    LoanstoTA             0.7004      0.6974      13.0000     158.9819    0.2569    
## ------------------------------------------------------------------------------------

Regression

On winsorised sample

fe_win_within <- plm(RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct + FED_rate, data = data_stata_win_reg, model = "within")

summary(fe_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + LongTermDebt_pct + NonIntInc_pct + Inflation + 
##     GDP_pct + FED_rate, data = data_stata_win_reg, model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -18.43044  -0.84523  -0.10495   0.66719  28.06779 
## 
## Coefficients:
##                   Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -0.863974   0.319066  -2.7078  0.006871 ** 
## LtD              -0.017875   0.016389  -1.0907  0.275648    
## LoanstoTA        -0.016532   0.024013  -0.6885  0.491290    
## Efficiency       -0.254759   0.011615 -21.9336 < 2.2e-16 ***
## LeverageRatio    -0.264780   0.057800  -4.5810 5.123e-06 ***
## LoanLossProv_pct -3.920973   0.110767 -35.3984 < 2.2e-16 ***
## LongTermDebt_pct  0.030308   0.036380   0.8331  0.404963    
## NonIntInc_pct     0.078732   0.018101   4.3496 1.483e-05 ***
## Inflation         0.416178   0.129309   3.2185  0.001324 ** 
## GDP_pct           0.508912   0.198876   2.5589  0.010624 *  
## FED_rate          0.408264   0.239233   1.7066  0.088170 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    19068
## Residual Sum of Squares: 6845
## R-Squared:      0.64102
## Adj. R-Squared: 0.59266
## F-statistic: 190.416 on 11 and 1173 DF, p-value: < 2.22e-16

fe_win_within <- plm(RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg, model = "within")

summary(fe_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -18.51681  -0.85985  -0.10643   0.67884  28.00367 
## 
## Coefficients:
##                   Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -0.563780   0.256839  -2.1951   0.02835 *  
## LtD              -0.024043   0.010057  -2.3907   0.01697 *  
## Efficiency       -0.256342   0.011511 -22.2699 < 2.2e-16 ***
## LeverageRatio    -0.261744   0.056829  -4.6058 4.556e-06 ***
## LoanLossProv_pct -3.942435   0.107882 -36.5441 < 2.2e-16 ***
## NonIntInc_pct     0.078808   0.018045   4.3673 1.368e-05 ***
## Inflation         0.570824   0.092623   6.1629 9.796e-10 ***
## GDP_pct           0.721446   0.151821   4.7519 2.263e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    19068
## Residual Sum of Squares: 6867
## R-Squared:      0.63987
## Adj. R-Squared: 0.5924
## F-statistic: 261.182 on 8 and 1176 DF, p-value: < 2.22e-16

With size buckets

fe_win_within_size_buckets <- plm(RoE ~ TA_1 + TA_2 + TA_3 + TA_4 + LtD + LoanstoTA + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg, model = "within")

summary(fe_win_within_size_buckets)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA_1 + TA_2 + TA_3 + TA_4 + LtD + LoanstoTA + 
##     Efficiency + LeverageRatio + LoanLossProv_pct + LongTermDebt_pct + 
##     NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -18.475253  -0.855885  -0.093122   0.697793  27.910994 
## 
## Coefficients:
##                    Estimate Std. Error  t-value  Pr(>|t|)    
## TA_1              0.9636649  0.7127204   1.3521   0.17661    
## TA_2              1.0828930  0.6104854   1.7738   0.07635 .  
## TA_3              0.7249439  0.5500023   1.3181   0.18774    
## TA_4              0.2078394  0.4402462   0.4721   0.63694    
## LtD              -0.0219347  0.0163445  -1.3420   0.17985    
## LoanstoTA        -0.0088437  0.0233963  -0.3780   0.70550    
## Efficiency       -0.2561131  0.0115005 -22.2697 < 2.2e-16 ***
## LeverageRatio    -0.2695593  0.0582314  -4.6291 4.082e-06 ***
## LoanLossProv_pct -3.9379616  0.1078832 -36.5021 < 2.2e-16 ***
## LongTermDebt_pct  0.0311262  0.0365473   0.8517   0.39457    
## NonIntInc_pct     0.0795531  0.0181003   4.3951 1.208e-05 ***
## Inflation         0.5804500  0.0931711   6.2299 6.496e-10 ***
## GDP_pct           0.7078371  0.1514980   4.6723 3.324e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    19068
## Residual Sum of Squares: 6859.7
## R-Squared:      0.64025
## Adj. R-Squared: 0.59109
## F-statistic: 160.309 on 13 and 1171 DF, p-value: < 2.22e-16

large banks

LR effect much larger than for small banks

fe_win_within_large <- plm(RoE ~ LtD + LoanstoTA + Efficiency + LeverageRatio +  LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct + est_RW, data = data_stata_win_reg_large, model = "within")

summary(fe_win_within_large)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + LongTermDebt_pct + NonIntInc_pct + Inflation + 
##     GDP_pct + est_RW, data = data_stata_win_reg_large, model = "within")
## 
## Unbalanced Panel: n = 74, T = 6-9, N = 623
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -11.417314  -0.808043  -0.095962   0.684833  24.183388 
## 
## Coefficients:
##                   Estimate Std. Error  t-value  Pr(>|t|)    
## LtD              -0.011718   0.019833  -0.5908  0.554876    
## LoanstoTA        -0.046338   0.031174  -1.4864  0.137748    
## Efficiency       -0.258409   0.015779 -16.3768 < 2.2e-16 ***
## LeverageRatio    -0.532049   0.077592  -6.8570 1.932e-11 ***
## LoanLossProv_pct -3.243787   0.138608 -23.4026 < 2.2e-16 ***
## LongTermDebt_pct -0.023720   0.050047  -0.4740  0.635720    
## NonIntInc_pct     0.104693   0.025300   4.1381 4.063e-05 ***
## Inflation         0.591348   0.125586   4.7087 3.175e-06 ***
## GDP_pct           0.916899   0.197644   4.6391 4.397e-06 ***
## est_RW            0.036859   0.011628   3.1698  0.001612 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    7676.6
## Residual Sum of Squares: 2610
## R-Squared:      0.66001
## Adj. R-Squared: 0.60766
## F-statistic: 104.635 on 10 and 539 DF, p-value: < 2.22e-16

fe_win_within_large <- plm(RoE ~ LtD + LoanstoTA + Efficiency + T1_pct +  LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct + est_RW, data = data_stata_win_reg_large, model = "within")

summary(fe_win_within_large)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ LtD + LoanstoTA + Efficiency + T1_pct + LoanLossProv_pct + 
##     LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct + 
##     est_RW, data = data_stata_win_reg_large, model = "within")
## 
## Unbalanced Panel: n = 74, T = 6-9, N = 623
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -11.734656  -0.907406  -0.079009   0.669354  23.441760 
## 
## Coefficients:
##                    Estimate Std. Error  t-value  Pr(>|t|)    
## LtD              -0.0414755  0.0198462  -2.0898 0.0371001 *  
## LoanstoTA        -0.0304981  0.0324790  -0.9390 0.3481470    
## Efficiency       -0.2485885  0.0162156 -15.3302 < 2.2e-16 ***
## T1_pct           -0.2323297  0.0645489  -3.5993 0.0003485 ***
## LoanLossProv_pct -3.0914994  0.1419484 -21.7790 < 2.2e-16 ***
## LongTermDebt_pct -0.0042584  0.0514705  -0.0827 0.9340933    
## NonIntInc_pct     0.1050562  0.0261057   4.0243 6.534e-05 ***
## Inflation         0.5781802  0.1294374   4.4669 9.676e-06 ***
## GDP_pct           0.7644222  0.2026875   3.7714 0.0001803 ***
## est_RW            0.0023124  0.0122047   0.1895 0.8497987    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    7676.6
## Residual Sum of Squares: 2771
## R-Squared:      0.63903
## Adj. R-Squared: 0.58344
## F-statistic: 95.4199 on 10 and 539 DF, p-value: < 2.22e-16

small banks

fe_win_within_small <- plm(RoE ~ LtD + LoanstoTA + Efficiency +  LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct + est_RW, data = data_stata_win_reg_small, model = "within")

summary(fe_win_within_small)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + LongTermDebt_pct + NonIntInc_pct + Inflation + 
##     GDP_pct + est_RW, data = data_stata_win_reg_small, model = "within")
## 
## Unbalanced Panel: n = 74, T = 7-9, N = 648
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -16.84155  -0.91748  -0.11930   0.83314  17.60955 
## 
## Coefficients:
##                    Estimate Std. Error  t-value  Pr(>|t|)    
## LtD              -0.0176585  0.0320195  -0.5515  0.581514    
## LoanstoTA        -0.0160934  0.0448215  -0.3591  0.719689    
## Efficiency       -0.2625698  0.0177499 -14.7928 < 2.2e-16 ***
## LeverageRatio    -0.1665510  0.0905967  -1.8384  0.066532 .  
## LoanLossProv_pct -4.6379699  0.1715886 -27.0296 < 2.2e-16 ***
## LongTermDebt_pct  0.0354611  0.0548854   0.6461  0.518482    
## NonIntInc_pct     0.0725226  0.0271240   2.6737  0.007718 ** 
## Inflation         0.5841923  0.1472116   3.9684  8.17e-05 ***
## GDP_pct           0.3618509  0.2298033   1.5746  0.115907    
## est_RW           -0.0034617  0.0169842  -0.2038  0.838569    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    10884
## Residual Sum of Squares: 3716.4
## R-Squared:      0.65856
## Adj. R-Squared: 0.60831
## F-statistic: 108.782 on 10 and 564 DF, p-value: < 2.22e-16

fe_win_within_small <- plm(RoE ~ LtD + LoanstoTA + Efficiency +  T1_pct + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct + est_RW, data = data_stata_win_reg_small, model = "within")

summary(fe_win_within_small)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ LtD + LoanstoTA + Efficiency + T1_pct + LoanLossProv_pct + 
##     LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct + 
##     est_RW, data = data_stata_win_reg_small, model = "within")
## 
## Unbalanced Panel: n = 74, T = 7-9, N = 648
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -16.69793  -0.94223  -0.14905   0.86000  17.73944 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## LtD              -0.02862755  0.03162570  -0.9052 0.3657464    
## LoanstoTA         0.00442590  0.04439323   0.0997 0.9206197    
## Efficiency       -0.25982846  0.01776288 -14.6276 < 2.2e-16 ***
## T1_pct            0.00058093  0.06739566   0.0086 0.9931256    
## LoanLossProv_pct -4.59854575  0.17267904 -26.6306 < 2.2e-16 ***
## LongTermDebt_pct  0.02686797  0.05542203   0.4848 0.6280145    
## NonIntInc_pct     0.07300970  0.02741320   2.6633 0.0079588 ** 
## Inflation         0.53032583  0.14540675   3.6472 0.0002897 ***
## GDP_pct           0.29675953  0.22791943   1.3020 0.1934352    
## est_RW           -0.01255799  0.01692172  -0.7421 0.4583219    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    10884
## Residual Sum of Squares: 3738.7
## R-Squared:      0.65651
## Adj. R-Squared: 0.60596
## F-statistic: 107.798 on 10 and 564 DF, p-value: < 2.22e-16

interaction between large banks and LR

fe_win_within_large_interaction <- plm(RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct + TA_large*LeverageRatio, data = data_stata_win_reg, model = "within")

summary(fe_win_within_large_interaction)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + LongTermDebt_pct + NonIntInc_pct + Inflation + 
##     GDP_pct + TA_large * LeverageRatio, data = data_stata_win_reg, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -18.09350  -0.85399  -0.12553   0.66617  27.56110 
## 
## Coefficients:
##                         Estimate Std. Error  t-value  Pr(>|t|)    
## TA                     -0.464867   0.259163  -1.7937 0.0731150 .  
## LtD                    -0.017445   0.016229  -1.0749 0.2826182    
## LoanstoTA              -0.011377   0.023229  -0.4898 0.6243987    
## Efficiency             -0.255768   0.011488 -22.2639 < 2.2e-16 ***
## LeverageRatio          -0.072562   0.077190  -0.9400 0.3473895    
## LoanLossProv_pct       -3.943659   0.108430 -36.3704 < 2.2e-16 ***
## LongTermDebt_pct        0.018758   0.036255   0.5174 0.6049811    
## NonIntInc_pct           0.081797   0.018036   4.5351 6.347e-06 ***
## Inflation               0.557859   0.092273   6.0457 1.996e-09 ***
## GDP_pct                 0.700591   0.151512   4.6240 4.182e-06 ***
## LeverageRatio:TA_large -0.405739   0.107124  -3.7876 0.0001599 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    19068
## Residual Sum of Squares: 6779.1
## R-Squared:      0.64447
## Adj. R-Squared: 0.59659
## F-statistic: 193.304 on 11 and 1173 DF, p-value: < 2.22e-16

Just being large or just having a high leverage ratio increases RoE. But having both decreases RoE. Hard to interpret.

fe_win_within_TA_interaction <- plm(RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct + TA*LeverageRatio, data = data_stata_win_reg, model = "within")

summary(fe_win_within_TA_interaction)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + LongTermDebt_pct + NonIntInc_pct + Inflation + 
##     GDP_pct + TA * LeverageRatio, data = data_stata_win_reg, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -17.83132  -0.81095  -0.11800   0.68606  27.75257 
## 
## Coefficients:
##                    Estimate Std. Error  t-value  Pr(>|t|)    
## TA                1.9715075  0.5379694   3.6647 0.0002587 ***
## LtD              -0.0129338  0.0161778  -0.7995 0.4241741    
## LoanstoTA        -0.0182714  0.0231628  -0.7888 0.4303738    
## Efficiency       -0.2551373  0.0114214 -22.3385 < 2.2e-16 ***
## LeverageRatio     4.4188913  0.8815117   5.0129 6.188e-07 ***
## LoanLossProv_pct -3.9507197  0.1077545 -36.6641 < 2.2e-16 ***
## LongTermDebt_pct  0.0048958  0.0362202   0.1352 0.8925024    
## NonIntInc_pct     0.0837494  0.0179341   4.6698 3.362e-06 ***
## Inflation         0.5648251  0.0916815   6.1607 9.935e-10 ***
## GDP_pct           0.7190349  0.1504657   4.7787 1.987e-06 ***
## TA:LeverageRatio -0.2070409  0.0388614  -5.3277 1.192e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    19068
## Residual Sum of Squares: 6699.9
## R-Squared:      0.64863
## Adj. R-Squared: 0.6013
## F-statistic: 196.85 on 11 and 1173 DF, p-value: < 2.22e-16

interaction in ‘changes’ regression

fe_changes_within_TA_interaction <- plm(RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct + TA*LeverageRatio, data = data_stata_changes_reg, model = "within")

summary(fe_changes_within_TA_interaction)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + LongTermDebt_pct + NonIntInc_pct + Inflation + 
##     GDP_pct + TA * LeverageRatio, data = data_stata_changes_reg, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 8, N = 1184
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -24.648002  -0.762168   0.051927   0.804613  31.998188 
## 
## Coefficients:
##                   Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -0.239929   0.989444  -0.2425 0.8084503    
## LtD              -0.049708   0.029172  -1.7040 0.0886884 .  
## LoanstoTA        -0.047099   0.046930  -1.0036 0.3158017    
## Efficiency       -0.208476   0.015983 -13.0437 < 2.2e-16 ***
## LeverageRatio    -0.010777   0.121912  -0.0884 0.9295747    
## LoanLossProv_pct -3.517741   0.175533 -20.0404 < 2.2e-16 ***
## LongTermDebt_pct  0.016481   0.055589   0.2965 0.7669285    
## NonIntInc_pct     0.070511   0.025384   2.7778 0.0055726 ** 
## Inflation         0.439690   0.120285   3.6554 0.0002698 ***
## GDP_pct           0.803846   0.195011   4.1221 4.058e-05 ***
## TA:LeverageRatio  0.245636   0.403027   0.6095 0.5423425    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    16720
## Residual Sum of Squares: 10254
## R-Squared:      0.38672
## Adj. R-Squared: 0.29218
## F-statistic: 58.7578 on 11 and 1025 DF, p-value: < 2.22e-16

plain ‘changes’ regression

Not significant effect anymore

fe_changes_within <- plm(RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_changes_reg, model = "within")

summary(fe_changes_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + LongTermDebt_pct + NonIntInc_pct + Inflation + 
##     GDP_pct, data = data_stata_changes_reg, model = "within")
## 
## Balanced Panel: n = 148, T = 8, N = 1184
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -24.45982  -0.75937   0.05584   0.79372  32.07902 
## 
## Coefficients:
##                    Estimate Std. Error  t-value  Pr(>|t|)    
## TA                0.0064587  0.9028143   0.0072 0.9942934    
## LtD              -0.0478119  0.0289963  -1.6489 0.0994753 .  
## LoanstoTA        -0.0487267  0.0468395  -1.0403 0.2984504    
## Efficiency       -0.2090892  0.0159462 -13.1122 < 2.2e-16 ***
## LeverageRatio     0.0364249  0.0941233   0.3870 0.6988432    
## LoanLossProv_pct -3.5016835  0.1734912 -20.1836 < 2.2e-16 ***
## LongTermDebt_pct  0.0151989  0.0555326   0.2737 0.7843750    
## NonIntInc_pct     0.0694600  0.0253174   2.7436 0.0061834 ** 
## Inflation         0.4438072  0.1200581   3.6966 0.0002301 ***
## GDP_pct           0.8016603  0.1949180   4.1128 4.222e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    16720
## Residual Sum of Squares: 10258
## R-Squared:      0.3865
## Adj. R-Squared: 0.29262
## F-statistic: 64.636 on 10 and 1026 DF, p-value: < 2.22e-16

Pre 2015 sample

Having fewer Loans to Deposits was better in “bad” times

fe_win_within_pre <- plm(RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg_pre, model = "within")

summary(fe_win_within_pre)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg_pre, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 5, N = 740
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -17.567451  -0.796309  -0.082795   0.760486  24.441989 
## 
## Coefficients:
##                   Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -0.726565   0.704036  -1.0320  0.302500    
## LtD              -0.046716   0.020127  -2.3210  0.020630 *  
## Efficiency       -0.332153   0.021137 -15.7144 < 2.2e-16 ***
## LeverageRatio    -0.042468   0.108575  -0.3911  0.695838    
## LoanLossProv_pct -4.013115   0.164004 -24.4696 < 2.2e-16 ***
## LongTermDebt_pct  0.095027   0.058677   1.6195  0.105883    
## NonIntInc_pct     0.090423   0.032317   2.7980  0.005312 ** 
## Inflation        -0.111602   0.264743  -0.4215  0.673512    
## GDP_pct          -0.566837   0.456230  -1.2424  0.214575    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    13469
## Residual Sum of Squares: 5002.6
## R-Squared:      0.62859
## Adj. R-Squared: 0.52921
## F-statistic: 109.632 on 9 and 583 DF, p-value: < 2.22e-16

post (inclding) 2015 sample

Negative effect of LR only in recent “good” times

fe_win_within_post <- plm(RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg_post, model = "within")

summary(fe_win_within_post)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg_post, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 4, N = 592
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -5.036583 -0.620436 -0.050682  0.487804  5.752468 
## 
## Coefficients:
##                    Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -0.2822422  0.5310816  -0.5314   0.59538    
## LtD               0.0009352  0.0147233   0.0635   0.94938    
## Efficiency       -0.1408133  0.0134144 -10.4971 < 2.2e-16 ***
## LeverageRatio    -0.3088197  0.0742547  -4.1589 3.853e-05 ***
## LoanLossProv_pct -3.1586843  0.5101364  -6.1918 1.377e-09 ***
## LongTermDebt_pct  0.0415394  0.0426692   0.9735   0.33084    
## NonIntInc_pct     0.0541944  0.0222955   2.4307   0.01547 *  
## Inflation         0.7238512  0.0888424   8.1476 3.978e-15 ***
## GDP_pct           1.0017963  0.0914847  10.9504 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1230.1
## Residual Sum of Squares: 555.49
## R-Squared:      0.54842
## Adj. R-Squared: 0.38648
## F-statistic: 58.6987 on 9 and 435 DF, p-value: < 2.22e-16

99% percentile winsorised sample vs

fe_win_within <- plm(RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg, model = "within")

summary(fe_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + LongTermDebt_pct + NonIntInc_pct + Inflation + 
##     GDP_pct, data = data_stata_win_reg, model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -18.48964  -0.85775  -0.10251   0.67267  28.03657 
## 
## Coefficients:
##                    Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -0.5471732  0.2597143  -2.1068   0.03534 *  
## LtD              -0.0211176  0.0162915  -1.2962   0.19515    
## LoanstoTA        -0.0066837  0.0233279  -0.2865   0.77454    
## Efficiency       -0.2570244  0.0115483 -22.2565 < 2.2e-16 ***
## LeverageRatio    -0.2676272  0.0578230  -4.6284 4.095e-06 ***
## LoanLossProv_pct -3.9554255  0.1090003 -36.2882 < 2.2e-16 ***
## LongTermDebt_pct  0.0278314  0.0363805   0.7650   0.44442    
## NonIntInc_pct     0.0776885  0.0181055   4.2909 1.926e-05 ***
## Inflation         0.5700913  0.0927392   6.1473 1.079e-09 ***
## GDP_pct           0.7276180  0.1522017   4.7806 1.969e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    19068
## Residual Sum of Squares: 6862
## R-Squared:      0.64013
## Adj. R-Squared: 0.592
## F-statistic: 208.826 on 10 and 1174 DF, p-value: < 2.22e-16

z-score >3 winsorised sample

fe_z_win_within <- plm(RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, model = "within")

summary(fe_z_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -1.651577 -0.125536 -0.018194  0.097316  3.480607 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA               -0.11690602  0.03724173  -3.1391 0.0017368 ** 
## LtD              -0.00072611  0.00030908  -2.3492 0.0189761 *  
## Efficiency       -0.03794052  0.00167286 -22.6801 < 2.2e-16 ***
## LeverageRatio    -0.00063090  0.00018206  -3.4654 0.0005485 ***
## LoanLossProv_pct -0.00482294  0.00014595 -33.0444 < 2.2e-16 ***
## NonIntInc_pct     0.00102781  0.00029044   3.5388 0.0004176 ***
## Inflation         0.06402162  0.01054012   6.0741 1.681e-09 ***
## GDP_pct           0.05095983  0.01058385   4.8149 1.665e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    352.01
## Residual Sum of Squares: 140.04
## R-Squared:      0.60218
## Adj. R-Squared: 0.54975
## F-statistic: 222.513 on 8 and 1176 DF, p-value: < 2.22e-16

fe_z_win_within <- plm(RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + NonIntInc_pct + LoanstoTA + LongTermDebt_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, model = "within")

summary(fe_z_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     NonIntInc_pct + LoanstoTA + LongTermDebt_pct + Inflation + 
##     GDP_pct, data = data_stata_z_win_reg, model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -1.642449 -0.126181 -0.017243  0.097592  3.479637 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA               -0.11418392  0.03762503  -3.0348 0.0024600 ** 
## LtD              -0.00054399  0.00049008  -1.1100 0.2672268    
## Efficiency       -0.03801235  0.00168062 -22.6181 < 2.2e-16 ***
## LeverageRatio    -0.00064975  0.00018487  -3.5146 0.0004572 ***
## LoanLossProv_pct -0.00484012  0.00014790 -32.7260 < 2.2e-16 ***
## NonIntInc_pct     0.00101213  0.00029143   3.4730 0.0005334 ***
## LoanstoTA        -0.00019661  0.00038581  -0.5096 0.6104119    
## LongTermDebt_pct  0.00011542  0.00028492   0.4051 0.6854899    
## Inflation         0.06386681  0.01055551   6.0506 1.938e-09 ***
## GDP_pct           0.05144893  0.01061467   4.8470 1.422e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    352.01
## Residual Sum of Squares: 139.97
## R-Squared:      0.60236
## Adj. R-Squared: 0.54919
## F-statistic: 177.844 on 10 and 1174 DF, p-value: < 2.22e-16

z-score >3 by year winsorised sample

fe_z_year_win_within <- plm(RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_year_win_reg , model = "within")

summary(fe_z_year_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_year_win_reg, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -36.44226  -0.89415  -0.12863   0.74830  25.85385 
## 
## Coefficients:
##                   Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -1.331815   0.293006  -4.5453 6.051e-06 ***
## LtD              -0.020466   0.011003  -1.8600   0.06313 .  
## Efficiency       -0.279868   0.013041 -21.4613 < 2.2e-16 ***
## LeverageRatio    -0.112365   0.065243  -1.7222   0.08529 .  
## LoanLossProv_pct -4.557797   0.129874 -35.0939 < 2.2e-16 ***
## NonIntInc_pct     0.079791   0.019997   3.9902 7.009e-05 ***
## Inflation         0.626420   0.105718   5.9254 4.087e-09 ***
## GDP_pct           0.679359   0.173470   3.9163 9.509e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    23724
## Residual Sum of Squares: 8969.5
## R-Squared:      0.62193
## Adj. R-Squared: 0.57209
## F-statistic: 241.812 on 8 and 1176 DF, p-value: < 2.22e-16

impact of estimated Risk weights

on own mildly significant

fe_z_win_within <- plm(RoE ~ TA + LtD + Efficiency + est_RW + LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, model = "within")

summary(fe_z_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + Efficiency + est_RW + LoanLossProv_pct + 
##     NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, 
##     model = "within")
## 
## Unbalanced Panel: n = 148, T = 6-9, N = 1271
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -1.570306 -0.126926 -0.022207  0.104576  3.482553 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA               -0.16780763  0.03878424  -4.3267 1.649e-05 ***
## LtD              -0.00088192  0.00033647  -2.6211 0.0088842 ** 
## Efficiency       -0.03825327  0.00178649 -21.4125 < 2.2e-16 ***
## est_RW            0.00258866  0.00135172   1.9151 0.0557383 .  
## LoanLossProv_pct -0.00476807  0.00015438 -30.8856 < 2.2e-16 ***
## NonIntInc_pct     0.00106471  0.00030482   3.4929 0.0004966 ***
## Inflation         0.06272209  0.01112743   5.6367 2.195e-08 ***
## GDP_pct           0.04828068  0.01088943   4.4337 1.018e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    341.79
## Residual Sum of Squares: 136.97
## R-Squared:      0.59926
## Adj. R-Squared: 0.54355
## F-statistic: 208.419 on 8 and 1115 DF, p-value: < 2.22e-16

with LR highly significant and positive.

fe_z_win_within <- plm(RoE ~ TA + LtD + Efficiency + LeverageRatio + est_RW + LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, model = "within")

summary(fe_z_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + Efficiency + LeverageRatio + est_RW + 
##     LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, 
##     model = "within")
## 
## Unbalanced Panel: n = 148, T = 6-9, N = 1271
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -1.626632 -0.123223 -0.019827  0.095260  3.402844 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA               -0.14512249  0.03895676  -3.7252 0.0002049 ***
## LtD              -0.00088737  0.00033429  -2.6545 0.0080555 ** 
## Efficiency       -0.03879748  0.00178021 -21.7938 < 2.2e-16 ***
## LeverageRatio    -0.00074921  0.00018945  -3.9547 8.148e-05 ***
## est_RW            0.00350251  0.00136267   2.5703 0.0102893 *  
## LoanLossProv_pct -0.00480721  0.00015369 -31.2778 < 2.2e-16 ***
## NonIntInc_pct     0.00110382  0.00030300   3.6429 0.0002820 ***
## Inflation         0.06764314  0.01112491   6.0803 1.645e-09 ***
## GDP_pct           0.05163314  0.01085180   4.7580 2.212e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    341.79
## Residual Sum of Squares: 135.07
## R-Squared:      0.60481
## Adj. R-Squared: 0.54947
## F-statistic: 189.432 on 9 and 1114 DF, p-value: < 2.22e-16

year lag

fe_win_lag_within <- plm(RoE ~ TA + LtD + Efficiency + LeverageRatio + NonPerfLoans_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_lag_reg, model = "within")

summary(fe_win_lag_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + Efficiency + LeverageRatio + NonPerfLoans_pct + 
##     NonIntInc_pct + Inflation + GDP_pct, data = data_stata_lag_reg, 
##     model = "within")
## 
## Unbalanced Panel: n = 148, T = 2-8, N = 1059
## 
## Residuals:
##        Min.     1st Qu.      Median     3rd Qu.        Max. 
## -23.8016018  -0.8495670   0.0074348   0.8405250  18.5498369 
## 
## Coefficients:
##                    Estimate Std. Error t-value  Pr(>|t|)    
## TA                0.1820368  0.3873171  0.4700    0.6385    
## LtD              -0.0074041  0.0128390 -0.5767    0.5643    
## Efficiency       -0.0735837  0.0151392 -4.8605 1.381e-06 ***
## LeverageRatio    -0.4212981  0.0741571 -5.6812 1.804e-08 ***
## NonPerfLoans_pct -0.4609852  0.0584556 -7.8861 8.974e-15 ***
## NonIntInc_pct     0.0199236  0.0231235  0.8616    0.3891    
## Inflation         0.1432377  0.1062939  1.3476    0.1781    
## GDP_pct           1.0462641  0.1815904  5.7617 1.142e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    7541.2
## Residual Sum of Squares: 6052.2
## R-Squared:      0.19745
## Adj. R-Squared: 0.059689
## F-statistic: 27.77 on 8 and 903 DF, p-value: < 2.22e-16

RoA

Pre 2015 sample

Having fewer Loans to Deposits was better in “bad” times

fe_win_within_pre <- plm(RoA ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg_pre, model = "within")

summary(fe_win_within_pre)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoA ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg_pre, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 5, N = 740
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -1.5501467 -0.0717446 -0.0011165  0.0664116  1.8374819 
## 
## Coefficients:
##                    Estimate Std. Error  t-value  Pr(>|t|)    
## TA                0.0752881  0.0635784   1.1842  0.236826    
## LtD              -0.0034565  0.0018176  -1.9017  0.057706 .  
## Efficiency       -0.0331206  0.0019088 -17.3517 < 2.2e-16 ***
## LeverageRatio     0.0260569  0.0098050   2.6575  0.008088 ** 
## LoanLossProv_pct -0.3814612  0.0148105 -25.7562 < 2.2e-16 ***
## LongTermDebt_pct  0.0060285  0.0052989   1.1377  0.255718    
## NonIntInc_pct     0.0069085  0.0029184   2.3672  0.018249 *  
## Inflation        -0.0152636  0.0239078  -0.6384  0.523440    
## GDP_pct          -0.0459865  0.0412001  -1.1162  0.264807    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    124.79
## Residual Sum of Squares: 40.796
## R-Squared:      0.67307
## Adj. R-Squared: 0.58559
## F-statistic: 133.361 on 9 and 583 DF, p-value: < 2.22e-16

post (including) 2015 sample

Negative effect of LR only in recent “good” times

fe_win_within_post <- plm(RoA ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg_post, model = "within")

summary(fe_win_within_post)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoA ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg_post, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 4, N = 592
## 
## Residuals:
##        Min.     1st Qu.      Median     3rd Qu.        Max. 
## -0.34558099 -0.05401360  0.00017307  0.04762960  0.69909600 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA               -0.00659729  0.04957027  -0.1331  0.894184    
## LtD               0.00130083  0.00137425   0.9466  0.344379    
## Efficiency       -0.01503268  0.00125208 -12.0062 < 2.2e-16 ***
## LeverageRatio     0.01970112  0.00693081   2.8425  0.004686 ** 
## LoanLossProv_pct -0.41837253  0.04761528  -8.7865 < 2.2e-16 ***
## LongTermDebt_pct  0.00051583  0.00398267   0.1295  0.897007    
## NonIntInc_pct     0.00381221  0.00208103   1.8319  0.067651 .  
## Inflation         0.07009467  0.00829240   8.4529 4.328e-16 ***
## GDP_pct           0.10817136  0.00853902  12.6679 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    14.887
## Residual Sum of Squares: 4.8395
## R-Squared:      0.67492
## Adj. R-Squared: 0.55834
## F-statistic: 100.348 on 9 and 435 DF, p-value: < 2.22e-16

99% percentile winsorised sample vs

fe_win_within <- plm(RoA ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + LoanLossProv_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg, model = "within")

summary(fe_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoA ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + LongTermDebt_pct + NonIntInc_pct + Inflation + 
##     GDP_pct, data = data_stata_win_reg, model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -2.0042407 -0.0791299 -0.0034487  0.0628206  2.2057718 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA                0.02479769  0.02388842   1.0381 0.2994544    
## LtD              -0.00511315  0.00149848  -3.4122 0.0006663 ***
## LoanstoTA         0.00568357  0.00214569   2.6488 0.0081854 ** 
## Efficiency       -0.02551588  0.00106221 -24.0215 < 2.2e-16 ***
## LeverageRatio     0.01912214  0.00531854   3.5954 0.0003374 ***
## LoanLossProv_pct -0.37293305  0.01002580 -37.1973 < 2.2e-16 ***
## LongTermDebt_pct  0.00024247  0.00334626   0.0725 0.9422480    
## NonIntInc_pct     0.00733575  0.00166534   4.4050 1.155e-05 ***
## Inflation         0.05285569  0.00853012   6.1964 7.983e-10 ***
## GDP_pct           0.08137045  0.01399946   5.8124 7.927e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    191.41
## Residual Sum of Squares: 58.054
## R-Squared:      0.6967
## Adj. R-Squared: 0.65614
## F-statistic: 269.671 on 10 and 1174 DF, p-value: < 2.22e-16

z-score >3 winsorised sample

fe_z_win_within <- plm(RoA ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, model = "within")

summary(fe_z_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoA ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -2.864115 -0.145569 -0.011503  0.115404  3.545609 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA                0.01984503  0.04238683   0.4682 0.6397365    
## LtD              -0.00051789  0.00035178  -1.4722 0.1412334    
## Efficiency       -0.04525092  0.00190397 -23.7666 < 2.2e-16 ***
## LeverageRatio     0.00086049  0.00020721   4.1528 3.522e-05 ***
## LoanLossProv_pct -0.00569352  0.00016612 -34.2741 < 2.2e-16 ***
## NonIntInc_pct     0.00121029  0.00033056   3.6613 0.0002621 ***
## Inflation         0.07616166  0.01199628   6.3488 3.093e-10 ***
## GDP_pct           0.07526315  0.01204605   6.2480 5.803e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    540.31
## Residual Sum of Squares: 181.4
## R-Squared:      0.66426
## Adj. R-Squared: 0.62001
## F-statistic: 290.838 on 8 and 1176 DF, p-value: < 2.22e-16

fe_z_win_within <- plm(RoA ~ TA + LtD + Efficiency + LeverageRatio +  LoanLossProv_pct + NonIntInc_pct + LoanstoTA + LongTermDebt_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, model = "within")

summary(fe_z_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoA ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     NonIntInc_pct + LoanstoTA + LongTermDebt_pct + Inflation + 
##     GDP_pct, data = data_stata_z_win_reg, model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -2.7266267 -0.1417871 -0.0063946  0.1120501  3.5514461 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA                0.00538748  0.04271457   0.1261 0.8996526    
## LtD              -0.00154681  0.00055637  -2.7802 0.0055199 ** 
## Efficiency       -0.04515985  0.00190795 -23.6693 < 2.2e-16 ***
## LeverageRatio     0.00095110  0.00020988   4.5316 6.453e-06 ***
## LoanLossProv_pct -0.00563297  0.00016791 -33.5486 < 2.2e-16 ***
## NonIntInc_pct     0.00127049  0.00033085   3.8401 0.0001295 ***
## LoanstoTA         0.00106494  0.00043799   2.4314 0.0151891 *  
## LongTermDebt_pct -0.00007108  0.00032346  -0.2197 0.8261050    
## Inflation         0.07721902  0.01198336   6.4439 1.696e-10 ***
## GDP_pct           0.07319717  0.01205052   6.0742 1.681e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    540.31
## Residual Sum of Squares: 180.4
## R-Squared:      0.66611
## Adj. R-Squared: 0.62146
## F-statistic: 234.216 on 10 and 1174 DF, p-value: < 2.22e-16

z-score >3 by year winsorised sample

fe_z_year_win_within <- plm(RoA ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_year_win_reg , model = "within")

summary(fe_z_year_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoA ~ TA + LtD + Efficiency + LeverageRatio + LoanLossProv_pct + 
##     NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_year_win_reg, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -1.6081497 -0.0795517 -0.0060333  0.0611544  1.8874881 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA                0.00343535  0.02363688   0.1453  0.884468    
## LtD              -0.00109255  0.00088762  -1.2309  0.218614    
## Efficiency       -0.02603599  0.00105199 -24.7493 < 2.2e-16 ***
## LeverageRatio     0.01961562  0.00526321   3.7269  0.000203 ***
## LoanLossProv_pct -0.39358521  0.01047700 -37.5666 < 2.2e-16 ***
## NonIntInc_pct     0.00766031  0.00161313   4.7487 2.299e-06 ***
## Inflation         0.05515255  0.00852828   6.4670 1.462e-10 ***
## GDP_pct           0.08333564  0.01399387   5.9552 3.427e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    194.95
## Residual Sum of Squares: 58.371
## R-Squared:      0.70058
## Adj. R-Squared: 0.66112
## F-statistic: 343.951 on 8 and 1176 DF, p-value: < 2.22e-16

impact of estimated Risk weights

Both LR and RW have positive impact on RoA. Increasing LR positive even if controlling for extra risk taking vie RW.

fe_z_win_within <- plm(RoA ~ TA + LtD + Efficiency + LeverageRatio + est_RW + LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, model = "within")

summary(fe_z_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoA ~ TA + LtD + Efficiency + LeverageRatio + est_RW + 
##     LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, 
##     model = "within")
## 
## Unbalanced Panel: n = 148, T = 6-9, N = 1271
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -2.770200 -0.142200 -0.014167  0.119111  3.521284 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA               -0.01354695  0.04392752  -0.3084 0.7578408    
## LtD              -0.00075593  0.00037694  -2.0054 0.0451588 *  
## Efficiency       -0.04575822  0.00200736 -22.7953 < 2.2e-16 ***
## LeverageRatio     0.00069018  0.00021362   3.2309 0.0012703 ** 
## est_RW            0.00492744  0.00153655   3.2068 0.0013803 ** 
## LoanLossProv_pct -0.00565317  0.00017330 -32.6198 < 2.2e-16 ***
## NonIntInc_pct     0.00131213  0.00034167   3.8404 0.0001298 ***
## Inflation         0.08018778  0.01254441   6.3923 2.398e-10 ***
## GDP_pct           0.07675745  0.01223646   6.2728 5.064e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    521.48
## Residual Sum of Squares: 171.74
## R-Squared:      0.67066
## Adj. R-Squared: 0.62454
## F-statistic: 252.057 on 9 and 1114 DF, p-value: < 2.22e-16

fe_z_win_within <- plm(RoA ~ TA + LtD + Efficiency + T1_pct + est_RW + LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, model = "within")

summary(fe_z_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoA ~ TA + LtD + Efficiency + T1_pct + est_RW + 
##     LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_z_win_reg, 
##     model = "within")
## 
## Unbalanced Panel: n = 148, T = 6-9, N = 1271
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -2.749999 -0.148633 -0.014708  0.117186  3.508487 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA                0.02476368  0.04526536   0.5471 0.5844348    
## LtD              -0.00068310  0.00038221  -1.7872 0.0741721 .  
## Efficiency       -0.04601531  0.00201603 -22.8247 < 2.2e-16 ***
## T1_pct            0.03561315  0.02479684   1.4362 0.1512270    
## est_RW            0.00638489  0.00157924   4.0430 5.640e-05 ***
## LoanLossProv_pct -0.00567189  0.00017401 -32.5949 < 2.2e-16 ***
## NonIntInc_pct     0.00131122  0.00034373   3.8147 0.0001438 ***
## Inflation         0.08328509  0.01255227   6.6351 5.052e-11 ***
## GDP_pct           0.07914706  0.01225442   6.4587 1.575e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    521.48
## Residual Sum of Squares: 173.03
## R-Squared:      0.66819
## Adj. R-Squared: 0.62172
## F-statistic: 249.258 on 9 and 1114 DF, p-value: < 2.22e-16

Subset selection “best” model

fe_win_within_best <- plm(RoE ~ TA + LtD +LoanstoTA + Efficiency + LeverageRatio + LoanLossProv_pct + NonPerfLoans_pct  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg, model = "within")

summary(fe_win_within_best)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + NonPerfLoans_pct + LongTermDebt_pct + 
##     NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg, 
##     model = "within")
## 
## Unbalanced Panel: n = 148, T = 3-9, N = 1206
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -18.286153  -0.837518  -0.064745   0.651913  27.988909 
## 
## Coefficients:
##                   Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -0.561382   0.316541  -1.7735 0.0764381 .  
## LtD              -0.012702   0.017516  -0.7252 0.4685142    
## LoanstoTA        -0.034089   0.025222  -1.3515 0.1768168    
## Efficiency       -0.263574   0.013162 -20.0250 < 2.2e-16 ***
## LeverageRatio    -0.324778   0.065160  -4.9843 7.272e-07 ***
## LoanLossProv_pct -3.871610   0.148436 -26.0827 < 2.2e-16 ***
## NonPerfLoans_pct -0.089726   0.063647  -1.4097 0.1589115    
## LongTermDebt_pct  0.025053   0.037667   0.6651 0.5061264    
## NonIntInc_pct     0.076201   0.020032   3.8040 0.0001506 ***
## Inflation         0.567120   0.100056   5.6681 1.866e-08 ***
## GDP_pct           0.782321   0.158989   4.9206 1.002e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    16827
## Residual Sum of Squares: 6165.5
## R-Squared:      0.6336
## Adj. R-Squared: 0.57831
## F-statistic: 164.597 on 11 and 1047 DF, p-value: < 2.22e-16

Comparing within with two-ways estimation

fe_win_within <- plm(RoE ~ TA + LtD +LoanstoTA + Efficiency + LeverageRatio + LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg, model = "within")

summary(fe_win_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + LoanstoTA + Efficiency + LeverageRatio + 
##     LoanLossProv_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_win_reg, 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -18.505555  -0.861255  -0.098293   0.684229  27.988835 
## 
## Coefficients:
##                   Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -0.544488   0.259645  -2.0971    0.0362 *  
## LtD              -0.017836   0.015714  -1.1351    0.2566    
## LoanstoTA        -0.011539   0.022444  -0.5141    0.6073    
## Efficiency       -0.256369   0.011514 -22.2650 < 2.2e-16 ***
## LeverageRatio    -0.267146   0.057809  -4.6211 4.238e-06 ***
## LoanLossProv_pct -3.948910   0.108648 -36.3460 < 2.2e-16 ***
## NonIntInc_pct     0.078190   0.018090   4.3222 1.676e-05 ***
## Inflation         0.569084   0.092713   6.1381 1.140e-09 ***
## GDP_pct           0.726332   0.152166   4.7733 2.040e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    19068
## Residual Sum of Squares: 6865.4
## R-Squared:      0.63995
## Adj. R-Squared: 0.59214
## F-statistic: 232.046 on 9 and 1175 DF, p-value: < 2.22e-16

two-ways

Removes macro factors and replaces with year dummy.

fe_win_twoways <- plm(RoE ~ TA + Efficiency + NonIntInc_pct + LeverageRatio + LoanLossProv_pct + LtD, data = data_stata_win_reg, model = "within", effect = "twoways")

summary(fe_win_twoways)

## Twoways effects Within Model
## 
## Call:
## plm(formula = RoE ~ TA + Efficiency + NonIntInc_pct + LeverageRatio + 
##     LoanLossProv_pct + LtD, data = data_stata_win_reg, effect = "twoways", 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -18.65604  -0.82396  -0.08100   0.65406  28.01129 
## 
## Coefficients:
##                   Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -0.156654   0.359553  -0.4357   0.66314    
## Efficiency       -0.254396   0.011536 -22.0526 < 2.2e-16 ***
## NonIntInc_pct     0.085760   0.018336   4.6771 3.248e-06 ***
## LeverageRatio    -0.266556   0.056506  -4.7173 2.678e-06 ***
## LoanLossProv_pct -4.016691   0.136332 -29.4625 < 2.2e-16 ***
## LtD              -0.020413   0.010072  -2.0267   0.04292 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    14996
## Residual Sum of Squares: 6654.9
## R-Squared:      0.55623
## Adj. R-Squared: 0.49516
## F-statistic: 244.417 on 6 and 1170 DF, p-value: < 2.22e-16

#fixef(fe_win_twoways)

fe_win_twoways <- plm(RoE ~ TA + Efficiency + NonIntInc_pct + LeverageRatio + LoanLossProv_pct + LtD, data = data_stata_win_reg, model = "within", effect = "twoways")

summary(fe_win_twoways)

## Twoways effects Within Model
## 
## Call:
## plm(formula = RoE ~ TA + Efficiency + NonIntInc_pct + LeverageRatio + 
##     LoanLossProv_pct + LtD, data = data_stata_win_reg, effect = "twoways", 
##     model = "within")
## 
## Balanced Panel: n = 148, T = 9, N = 1332
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -18.65604  -0.82396  -0.08100   0.65406  28.01129 
## 
## Coefficients:
##                   Estimate Std. Error  t-value  Pr(>|t|)    
## TA               -0.156654   0.359553  -0.4357   0.66314    
## Efficiency       -0.254396   0.011536 -22.0526 < 2.2e-16 ***
## NonIntInc_pct     0.085760   0.018336   4.6771 3.248e-06 ***
## LeverageRatio    -0.266556   0.056506  -4.7173 2.678e-06 ***
## LoanLossProv_pct -4.016691   0.136332 -29.4625 < 2.2e-16 ***
## LtD              -0.020413   0.010072  -2.0267   0.04292 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    14996
## Residual Sum of Squares: 6654.9
## R-Squared:      0.55623
## Adj. R-Squared: 0.49516
## F-statistic: 244.417 on 6 and 1170 DF, p-value: < 2.22e-16

plmtest(fe_win_twoways, effect = "twoways")

## 
##  Lagrange Multiplier Test - two-ways effects (Honda) for balanced
##  panels
## 
## data:  RoE ~ TA + Efficiency + NonIntInc_pct + LeverageRatio + LoanLossProv_pct +  ...
## normal = 19.631, p-value < 2.2e-16
## alternative hypothesis: significant effects

pooling <- plm(RoE ~ TA + Efficiency + NonIntInc_pct + LeverageRatio + LoanLossProv_pct + LtD, data = data_stata_win_reg, model = "pooling")

pFtest(RoE ~ TA + Efficiency + NonIntInc_pct + LeverageRatio + LoanLossProv_pct + LtD, data = data_stata_win_reg, effect = "twoways")

## 
##  F test for twoways effects
## 
## data:  RoE ~ TA + Efficiency + NonIntInc_pct + LeverageRatio + LoanLossProv_pct +  ...
## F = 3.9041, df1 = 155, df2 = 1170, p-value < 2.2e-16
## alternative hypothesis: significant effects

pFtest(fe_win_twoways, pooling)

## 
##  F test for twoways effects
## 
## data:  RoE ~ TA + Efficiency + NonIntInc_pct + LeverageRatio + LoanLossProv_pct +  ...
## F = 3.9041, df1 = 155, df2 = 1170, p-value < 2.2e-16
## alternative hypothesis: significant effects

test2 <- read.csv("test_2.csv")

test2 <- lm(intercept ~ GDP_pct + Inflation, data = test2)

summary(test2)

## 
## Call:
## lm(formula = intercept ~ GDP_pct + Inflation, data = test2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.69132 -0.09168  0.12044  0.59221  0.95964 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)   1.0736     1.9809   0.542    0.607
## GDP_pct       0.3516     0.9158   0.384    0.714
## Inflation     0.6184     0.5613   1.102    0.313
## 
## Residual standard error: 1.282 on 6 degrees of freedom
## Multiple R-squared:  0.1687, Adjusted R-squared:  -0.1084 
## F-statistic: 0.6087 on 2 and 6 DF,  p-value: 0.5745

On non-winsorised sample

fe_within <- plm(RoE ~ TA + LtD +LoanstoTA + Efficiency + T1_pct + LoanLossProv_pct +  + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_reg, model = "within")

summary(fe_within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA + LtD + LoanstoTA + Efficiency + T1_pct + 
##     LoanLossProv_pct + +LongTermDebt_pct + NonIntInc_pct + Inflation + 
##     GDP_pct, data = data_stata_reg, model = "within")
## 
## Unbalanced Panel: n = 148, T = 6-9, N = 1271
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -72.56524  -1.10040  -0.13567   0.93075  35.01315 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA               -1.72996360  0.46117950  -3.7512 0.0001851 ***
## LtD               0.00096837  0.01301450   0.0744 0.9407002    
## LoanstoTA        -0.02138063  0.03197871  -0.6686 0.5038960    
## Efficiency       -0.32774991  0.01780462 -18.4081 < 2.2e-16 ***
## T1_pct            0.14271033  0.07686247   1.8567 0.0636183 .  
## LoanLossProv_pct -5.36960432  0.17921708 -29.9615 < 2.2e-16 ***
## LongTermDebt_pct  0.02129951  0.05840697   0.3647 0.7154239    
## NonIntInc_pct     0.08104736  0.03148046   2.5745 0.0101660 *  
## Inflation         0.60097470  0.16757817   3.5862 0.0003500 ***
## GDP_pct           0.55368580  0.26850891   2.0621 0.0394322 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    46186
## Residual Sum of Squares: 19780
## R-Squared:      0.57174
## Adj. R-Squared: 0.51133
## F-statistic: 148.587 on 10 and 1113 DF, p-value: < 2.22e-16

With size in 5 buckets

fe_within_size_buckets <- plm(RoE ~ TA_1 + TA_2 + TA_3 + TA_4 + LtD + LoanstoTA + Efficiency + T1_pct + LoanLossProv_pct + LongTermDebt_pct + NonIntInc_pct + Inflation + GDP_pct, data = data_stata_reg, model = "within")

summary(fe_within_size_buckets)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = RoE ~ TA_1 + TA_2 + TA_3 + TA_4 + LtD + LoanstoTA + 
##     Efficiency + T1_pct + LoanLossProv_pct + LongTermDebt_pct + 
##     NonIntInc_pct + Inflation + GDP_pct, data = data_stata_reg, 
##     model = "within")
## 
## Unbalanced Panel: n = 148, T = 6-9, N = 1271
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -72.66768  -1.10361  -0.14012   0.96900  34.73454 
## 
## Coefficients:
##                     Estimate  Std. Error  t-value  Pr(>|t|)    
## TA_1              3.22364905  1.28536752   2.5080 0.0122849 *  
## TA_2              2.73147613  1.11601481   2.4475 0.0145382 *  
## TA_3              2.55969027  0.99126413   2.5822 0.0099431 ** 
## TA_4              0.52452331  0.80919571   0.6482 0.5169875    
## LtD               0.00051007  0.01305594   0.0391 0.9688433    
## LoanstoTA        -0.02798746  0.03215026  -0.8705 0.3842043    
## Efficiency       -0.32600873  0.01783580 -18.2783 < 2.2e-16 ***
## T1_pct            0.16941727  0.07664527   2.2104 0.0272803 *  
## LoanLossProv_pct -5.30546719  0.17705426 -29.9652 < 2.2e-16 ***
## LongTermDebt_pct  0.02146024  0.05879640   0.3650 0.7151867    
## NonIntInc_pct     0.08816540  0.03150390   2.7986 0.0052220 ** 
## Inflation         0.63351059  0.16858128   3.7579 0.0001803 ***
## GDP_pct           0.48108131  0.26659758   1.8045 0.0714204 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    46186
## Residual Sum of Squares: 19783
## R-Squared:      0.57167
## Adj. R-Squared: 0.50993
## F-statistic: 113.957 on 13 and 1110 DF, p-value: < 2.22e-16

Reg on rows with winsorised variables

fe_win_nowin <- plm(roe ~ ta + ltd +loanstota + efficiency + t1_pct + loanlossprov_pct +  + longtermdebt_pct + nonintinc_pct + inflation + gdp_pct, data = residual_win_reg, model = "within")

summary(fe_win_nowin)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = roe ~ ta + ltd + loanstota + efficiency + t1_pct + 
##     loanlossprov_pct + +longtermdebt_pct + nonintinc_pct + inflation + 
##     gdp_pct, data = residual_win_reg, model = "within")
## 
## Unbalanced Panel: n = 65, T = 1-8, N = 164
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -39.2697  -1.8292   0.0000   1.7771  37.9599 
## 
## Coefficients:
##                     Estimate  Std. Error t-value  Pr(>|t|)    
## ta               -2.1833e-11  3.1598e-11 -0.6910   0.49138    
## ltd               8.8086e-03  7.1921e-02  0.1225   0.90280    
## loanstota        -7.3604e-02  1.8870e-01 -0.3901   0.69742    
## efficiency       -4.9418e-01  8.6576e-02 -5.7080 1.483e-07 ***
## t1_pct            7.1020e-01  4.2219e-01  1.6822   0.09604 .  
## loanlossprov_pct -7.3518e+00  8.0792e-01 -9.0997 2.335e-14 ***
## longtermdebt_pct  5.8520e-02  6.0780e-01  0.0963   0.92351    
## nonintinc_pct     2.5349e-01  2.2856e-01  1.1091   0.27038    
## inflation         1.2324e+00  1.5728e+00  0.7836   0.43535    
## gdp_pct           6.2590e-01  2.7406e+00  0.2284   0.81987    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    33677
## Residual Sum of Squares: 10637
## R-Squared:      0.68415
## Adj. R-Squared: 0.42153
## F-statistic: 19.2778 on 10 and 89 DF, p-value: < 2.22e-16

heteroskedasticity

residual_two_way %>%
  ggplot(aes(x = fited_roe, y = roe)) +
  geom_point()

residual_two_way %>%
  ggplot(aes(x = roe, y = r_roe)) +
  geom_point()